Metrika [SJR: 0.943] [H-I: 25] [2 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1435-926X - ISSN (Online) 0026-1335 Published by Springer-Verlag [2335 journals] |
- On runs of ones defined on a q -sequence of binary trials
- Abstract: Abstract
In a sequence of n binary (
\(0{-}1\)
) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k,
\(1\le k\le n\)
. Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this random variable. Statistical inference problems related to the probability of ones are examined by numerical techniques. Numerics illustrate further the theoretical results.
PubDate: 2016-07-01
- Abstract: Abstract
In a sequence of n binary (
\(0{-}1\)
) trials, with probability of ones varying according to a geometric rule, we consider a random variable denoting the number of runs of ones of length at least equal to a fixed threshold k,
\(1\le k\le n\)
. Closed and recursive expressions are obtained for the probability mass function, generating functions and moments of this random variable. Statistical inference problems related to the probability of ones are examined by numerical techniques. Numerics illustrate further the theoretical results.
- Stochastic somparisons of order statistics from scaled and interdependent
random variables- Abstract: Abstract
This paper studies order statistics from random variables following the scale model. In the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes and the second smallest order statistic, the dispersive order and the star order of the sample extremes.
PubDate: 2016-07-01
- Abstract: Abstract
This paper studies order statistics from random variables following the scale model. In the presence of the Archimedean copula or survival copula for the random variables, we obtain the usual stochastic order of the sample extremes and the second smallest order statistic, the dispersive order and the star order of the sample extremes.
- A mixture model of size-biased distributions
- Abstract: Abstract
In reliability and survival analysis, to model lifetime data, size-biased distributions are useful. In this paper, a mixture model of size-biased distributions is introduced and studied. Several reliability properties of this model are investigated. In addition, some implications of well-known stochastic orders and aging classes concerning the model are established. To underline the usefulness of the model, some examples of interest in reliability and statistics are given.
PubDate: 2016-07-01
- Abstract: Abstract
In reliability and survival analysis, to model lifetime data, size-biased distributions are useful. In this paper, a mixture model of size-biased distributions is introduced and studied. Several reliability properties of this model are investigated. In addition, some implications of well-known stochastic orders and aging classes concerning the model are established. To underline the usefulness of the model, some examples of interest in reliability and statistics are given.
- Single change-point detection methods for small lifetime samples
- Abstract: Abstract
In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some
\(k\in \{1,\ldots ,n\}\)
such that the common failure rate of the first k failure times is different from the common failure rate of the last
\(n-k\)
failure times, based on an exponential lifetime distribution. The statistical test we propose is based on the empirical average ratio under the assumption of exponentiality. The proposed test is compared to the one based on the Mann–Whitney statistic for which no parametric assumption on the underlying distribution is necessary. The proposed statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the n failure times which enables the determination of critical values of the proposed tests by Monte Carlo methods for small sample sizes.
PubDate: 2016-07-01
- Abstract: Abstract
In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some
\(k\in \{1,\ldots ,n\}\)
such that the common failure rate of the first k failure times is different from the common failure rate of the last
\(n-k\)
failure times, based on an exponential lifetime distribution. The statistical test we propose is based on the empirical average ratio under the assumption of exponentiality. The proposed test is compared to the one based on the Mann–Whitney statistic for which no parametric assumption on the underlying distribution is necessary. The proposed statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the n failure times which enables the determination of critical values of the proposed tests by Monte Carlo methods for small sample sizes.
- Asymptotic results of a nonparametric conditional cumulative distribution
estimator in the single functional index modeling for time series data
with applications- Abstract: Abstract
In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore, we provide some applications and simulations to illustrate our methodology.
PubDate: 2016-07-01
- Abstract: Abstract
In this paper, we treat nonparametric estimation of the conditional cumulative distribution with a scalar response variable conditioned by a functional Hilbertian regressor. We establish asymptotic normality and uniform almost complete convergence rates of the conditional cumulative distribution estimator for dependent variables, linked semiparametrically by the single index structure. Furthermore, we provide some applications and simulations to illustrate our methodology.
- A new method of kernel-smoothing estimation of the ROC curve
- Abstract: Abstract
The receiver operating characteristic (ROC) curve is a popular graphical tool for describing the accuracy of a diagnostic test. Based on the idea of estimating the ROC curve as a distribution function, we propose a new kernel smoothing estimator of the ROC curve which is invariant under nondecreasing data transformations. We prove that the estimator has better asymptotic mean squared error properties than some other estimators involving kernel smoothing and we present an easy method of bandwidth selection. By simulation studies, we show that for the limited sample sizes, our proposed estimator is competitive with some other nonparametric estimators of the ROC curve. We also give an example of applying the estimator to a real data set.
PubDate: 2016-07-01
- Abstract: Abstract
The receiver operating characteristic (ROC) curve is a popular graphical tool for describing the accuracy of a diagnostic test. Based on the idea of estimating the ROC curve as a distribution function, we propose a new kernel smoothing estimator of the ROC curve which is invariant under nondecreasing data transformations. We prove that the estimator has better asymptotic mean squared error properties than some other estimators involving kernel smoothing and we present an easy method of bandwidth selection. By simulation studies, we show that for the limited sample sizes, our proposed estimator is competitive with some other nonparametric estimators of the ROC curve. We also give an example of applying the estimator to a real data set.
- Conditional empirical likelihood for quantile regression models
- Abstract: Abstract
In this paper, we propose a new Bayesian quantile regression estimator using conditional empirical likelihood as the working likelihood function. We show that the proposed estimator is asymptotically efficient and the confidence interval constructed is asymptotically valid. Our estimator has low computation cost since the posterior distribution function has explicit form. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies.
PubDate: 2016-06-23
- Abstract: Abstract
In this paper, we propose a new Bayesian quantile regression estimator using conditional empirical likelihood as the working likelihood function. We show that the proposed estimator is asymptotically efficient and the confidence interval constructed is asymptotically valid. Our estimator has low computation cost since the posterior distribution function has explicit form. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies.
- Tree based diagnostic procedures following a smooth test of
goodness-of-fit- Abstract: Abstract
This paper introduces a statistical procedure, to be applied after a goodness-of-fit test has rejected a null model, that provides diagnostic information to help the user decide on a better model. The procedure goes through a list of departures, each being tested by a local smooth test. The list is organized into a hierarchy by seeking answers to the questions “Where is the problem?” and “What is the problem there?”. This hierarchy allows to focus on finer departures as the data becomes more abundant. The procedure controls the family-wise Type 1 error rate. Simulations show that the procedure can succeed in providing useful diagnostic information.
PubDate: 2016-06-10
- Abstract: Abstract
This paper introduces a statistical procedure, to be applied after a goodness-of-fit test has rejected a null model, that provides diagnostic information to help the user decide on a better model. The procedure goes through a list of departures, each being tested by a local smooth test. The list is organized into a hierarchy by seeking answers to the questions “Where is the problem?” and “What is the problem there?”. This hierarchy allows to focus on finer departures as the data becomes more abundant. The procedure controls the family-wise Type 1 error rate. Simulations show that the procedure can succeed in providing useful diagnostic information.
- Imputation based statistical inference for partially linear quantile
regression models with missing responses- Abstract: Abstract
In this paper, we consider the confidence interval construction for partially linear quantile regression models with missing response at random. We propose an imputation based empirical likelihood method to construct confidence intervals for the parametric components and the nonparametric components, and show that the proposed empirical log-likelihood ratios are both asymptotically Chi-squared in theory. Then, the confidence region for the parametric component and the pointwise confidence interval for the nonparametric component are constructed. Some simulation studies and a real data application are carried out to assess the performance of the proposed estimation method, and simulation results indicate that the proposed method is workable.
PubDate: 2016-06-09
- Abstract: Abstract
In this paper, we consider the confidence interval construction for partially linear quantile regression models with missing response at random. We propose an imputation based empirical likelihood method to construct confidence intervals for the parametric components and the nonparametric components, and show that the proposed empirical log-likelihood ratios are both asymptotically Chi-squared in theory. Then, the confidence region for the parametric component and the pointwise confidence interval for the nonparametric component are constructed. Some simulation studies and a real data application are carried out to assess the performance of the proposed estimation method, and simulation results indicate that the proposed method is workable.
- A test of linearity in partial functional linear regression
- Abstract: Abstract
This paper investigates the hypothesis test of the parametric component in partial functional linear regression. We propose a test procedure based on the residual sums of squares under the null and alternative hypothesis, and establish the asymptotic properties of the resulting test. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, we present an illustration through fitting the Berkeley growth data with a partial functional linear regression model and testing the effect of gender on the height of kids.
PubDate: 2016-06-08
- Abstract: Abstract
This paper investigates the hypothesis test of the parametric component in partial functional linear regression. We propose a test procedure based on the residual sums of squares under the null and alternative hypothesis, and establish the asymptotic properties of the resulting test. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. Finally, we present an illustration through fitting the Berkeley growth data with a partial functional linear regression model and testing the effect of gender on the height of kids.
- Nonparametric estimation in a mixed-effect Ornstein–Uhlenbeck model
- Abstract: Abstract
Two adaptive nonparametric procedures are proposed to estimate the density of the random effects in a mixed-effect Ornstein–Uhlenbeck model. First a kernel estimator is introduced with a new bandwidth selection method developed recently by Goldenshluger and Lepski (Ann Stat 39:1608–1632, 2011). Then, we adapt an estimator from Comte et al. (Stoch Process Appl 7:2522–2551, 2013) in the framework of small time interval of observation. More precisely, we propose an estimator that uses deconvolution tools and depends on two tuning parameters to be chosen in a data-driven way. The selection of these two parameters is achieved through a two-dimensional penalized criterion. For both adaptive estimators, risk bounds are provided in terms of integrated
\(\mathbb {L}^2\)
-error. The estimators are evaluated on simulations and show good results. Finally, these nonparametric estimators are applied to neuronal data and are compared with previous parametric estimations.
PubDate: 2016-05-23
- Abstract: Abstract
Two adaptive nonparametric procedures are proposed to estimate the density of the random effects in a mixed-effect Ornstein–Uhlenbeck model. First a kernel estimator is introduced with a new bandwidth selection method developed recently by Goldenshluger and Lepski (Ann Stat 39:1608–1632, 2011). Then, we adapt an estimator from Comte et al. (Stoch Process Appl 7:2522–2551, 2013) in the framework of small time interval of observation. More precisely, we propose an estimator that uses deconvolution tools and depends on two tuning parameters to be chosen in a data-driven way. The selection of these two parameters is achieved through a two-dimensional penalized criterion. For both adaptive estimators, risk bounds are provided in terms of integrated
\(\mathbb {L}^2\)
-error. The estimators are evaluated on simulations and show good results. Finally, these nonparametric estimators are applied to neuronal data and are compared with previous parametric estimations.
- Qualitative robustness of estimators on stochastic processes
- Abstract: Abstract
A lot of statistical methods originally designed for independent and identically distributed (i.i.d.) data are also successfully used for dependent observations. Still most theoretical investigations on robustness assume i.i.d. pairs of random variables. We examine an important property of statistical estimators—the qualitative robustness in the case of observations which do not fulfill the i.i.d. assumption. In the i.i.d. case qualitative robustness of a sequence of estimators is, according to Hampel (Ann Math Stat 42:1887–1896, 1971), ensured by continuity of the corresponding statistical functional. A similar result for the non-i.i.d. case is shown in this article. Continuity of the corresponding statistical functional still ensures qualitative robustness of the estimator as long as the data generating process satisfies a certain convergence condition on its empirical measure. Examples for processes providing such a convergence condition, including certain Markov chains or mixing processes, are given as well as examples for qualitatively robust estimators in the non-i.i.d. case.
PubDate: 2016-05-13
- Abstract: Abstract
A lot of statistical methods originally designed for independent and identically distributed (i.i.d.) data are also successfully used for dependent observations. Still most theoretical investigations on robustness assume i.i.d. pairs of random variables. We examine an important property of statistical estimators—the qualitative robustness in the case of observations which do not fulfill the i.i.d. assumption. In the i.i.d. case qualitative robustness of a sequence of estimators is, according to Hampel (Ann Math Stat 42:1887–1896, 1971), ensured by continuity of the corresponding statistical functional. A similar result for the non-i.i.d. case is shown in this article. Continuity of the corresponding statistical functional still ensures qualitative robustness of the estimator as long as the data generating process satisfies a certain convergence condition on its empirical measure. Examples for processes providing such a convergence condition, including certain Markov chains or mixing processes, are given as well as examples for qualitatively robust estimators in the non-i.i.d. case.
- A von Mises approximation to the small sample distribution of the trimmed
mean- Abstract: Abstract
The small sample distribution of the trimmed mean is usually approximated by a Student’s t distribution. But this approximation is valid only when the observations come from a standard normal model and the sample size is not very small. Moreover, until now, there is only empirical justification for this approximation but no formal proof. Although there are some accurate saddlepoint approximations when the sample size is small and the distribution not normal, these are very difficult to apply and the elements involved in it, difficult to interpret. In this paper we propose a new approximation based on the von Mises expansion for the tail probability functional of the trimmed mean, which improves the usual Student’s t approximation in the normal case and which can be applied for other models. This new approximation allows, for instance, an objective choice of the trimming fraction in a context of hypothesis testing problem using the new tool of the p value line.
PubDate: 2016-05-01
- Abstract: Abstract
The small sample distribution of the trimmed mean is usually approximated by a Student’s t distribution. But this approximation is valid only when the observations come from a standard normal model and the sample size is not very small. Moreover, until now, there is only empirical justification for this approximation but no formal proof. Although there are some accurate saddlepoint approximations when the sample size is small and the distribution not normal, these are very difficult to apply and the elements involved in it, difficult to interpret. In this paper we propose a new approximation based on the von Mises expansion for the tail probability functional of the trimmed mean, which improves the usual Student’s t approximation in the normal case and which can be applied for other models. This new approximation allows, for instance, an objective choice of the trimming fraction in a context of hypothesis testing problem using the new tool of the p value line.
- Fourier-type estimation of the power GARCH model with stable-Paretian
innovations- Abstract: Abstract
We consider estimation for general power GARCH models under stable-Paretian innovations. Exploiting the simple structure of the conditional characteristic function of the observations driven by these models we propose minimum distance estimation based on the empirical characteristic function of corresponding residuals. Consistency of the estimators is proved, and the asymptotic distribution of the estimator is studied. Efficiency issues are explored and finite-sample results are presented as well as applications of the proposed procedures to real data from the financial markets. A multivariate extension is also considered.
PubDate: 2016-05-01
- Abstract: Abstract
We consider estimation for general power GARCH models under stable-Paretian innovations. Exploiting the simple structure of the conditional characteristic function of the observations driven by these models we propose minimum distance estimation based on the empirical characteristic function of corresponding residuals. Consistency of the estimators is proved, and the asymptotic distribution of the estimator is studied. Efficiency issues are explored and finite-sample results are presented as well as applications of the proposed procedures to real data from the financial markets. A multivariate extension is also considered.
- Semiparametric estimation of a zero-inflated Poisson regression model with
missing covariates- Abstract: Abstract
Zero-inflated Poisson (ZIP) regression models have been widely used to study the effects of covariates in count data sets that have many zeros. However, often some covariates involved in ZIP regression modeling have missing values. Assuming that the selection probability is known or unknown and estimated via a non-parametric method, we propose the inverse probability weighting (IPW) method to estimate the parameters of the ZIP regression model with covariates missing at random. The asymptotic properties of the proposed estimators are studied in detail under certain regularity conditions. Both theoretical analysis and simulation results show that the semiparametric IPW estimator is more efficient than the true weight IPW estimator. The practical use of the proposed methodology is illustrated with data from a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.
PubDate: 2016-05-01
- Abstract: Abstract
Zero-inflated Poisson (ZIP) regression models have been widely used to study the effects of covariates in count data sets that have many zeros. However, often some covariates involved in ZIP regression modeling have missing values. Assuming that the selection probability is known or unknown and estimated via a non-parametric method, we propose the inverse probability weighting (IPW) method to estimate the parameters of the ZIP regression model with covariates missing at random. The asymptotic properties of the proposed estimators are studied in detail under certain regularity conditions. Both theoretical analysis and simulation results show that the semiparametric IPW estimator is more efficient than the true weight IPW estimator. The practical use of the proposed methodology is illustrated with data from a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.
- Minimum Hellinger distance estimation for bivariate samples and time
series with applications to nonlinear regression and copula-based models- Abstract: Abstract
We study minimum Hellinger distance estimation (MHDE) based on kernel density estimators for bivariate time series, such that various commonly used regression models and parametric time series such as nonlinear regressions with conditionally heteroscedastic errors and copula-based Markov processes, where copula densities are used to model the conditional densities, can be treated. It is shown that consistency and asymptotic normality of the MHDE basically follow from the uniform consistency of the density estimate and the validity of the central limit theorem for its integrated version. We also provide explicit sufficient conditions both for the i.i.d. case and the case of strong mixing series. In addition, for the case of i.i.d. data, we briefly discuss the asymptotics under local alternatives and relate the results to maximum likelihood estimation.
PubDate: 2016-05-01
- Abstract: Abstract
We study minimum Hellinger distance estimation (MHDE) based on kernel density estimators for bivariate time series, such that various commonly used regression models and parametric time series such as nonlinear regressions with conditionally heteroscedastic errors and copula-based Markov processes, where copula densities are used to model the conditional densities, can be treated. It is shown that consistency and asymptotic normality of the MHDE basically follow from the uniform consistency of the density estimate and the validity of the central limit theorem for its integrated version. We also provide explicit sufficient conditions both for the i.i.d. case and the case of strong mixing series. In addition, for the case of i.i.d. data, we briefly discuss the asymptotics under local alternatives and relate the results to maximum likelihood estimation.
- On the skewness of order statistics in multiple-outlier PHR models
- Abstract: Abstract
In this paper, we investigate the skewness of order statistics stemming from multiple-outlier proportional hazard rates samples in the sense of several variability orderings such as the star order, Lorenz order and dispersive order. It is shown that the more heterogeneity among the multiple-outlier components will lead to a more skewed lifetime of a k-out-of-n system consisting of these components. The results established here generalize the corresponding ones in Kochar and Xu (J Appl Probab 48:271–284, 2011, Ann Oper Res 212:127–138, 2014). Some numerical examples are also provided to illustrate the theoretical results.
PubDate: 2016-04-20
- Abstract: Abstract
In this paper, we investigate the skewness of order statistics stemming from multiple-outlier proportional hazard rates samples in the sense of several variability orderings such as the star order, Lorenz order and dispersive order. It is shown that the more heterogeneity among the multiple-outlier components will lead to a more skewed lifetime of a k-out-of-n system consisting of these components. The results established here generalize the corresponding ones in Kochar and Xu (J Appl Probab 48:271–284, 2011, Ann Oper Res 212:127–138, 2014). Some numerical examples are also provided to illustrate the theoretical results.
- Quantile inference based on clustered data
- Abstract: Abstract
One-sample sign test is one of the common procedures to develop distribution-free inference for a quantile of a population. A basic requirement of this test is that the observations in a sample must be independent. This assumption is violated in certain settings, such as clustered data, grouped data and longitudinal studies. Failure to account for dependence structure leads to erroneous statistical inferences. In this study, we have developed statistical inference for a population quantile of order p in either balanced or unbalanced designs by incorporating dependence structure when the distribution of within-cluster observations is exchangeable. We provide a point estimate, develop a testing procedure and construct confidence intervals for a population quantile of order p. Simulation studies are performed to demonstrate that the confidence intervals achieve their nominal coverage probabilities. We finally apply the proposed procedure to Academic Performance Index data.
PubDate: 2016-04-19
- Abstract: Abstract
One-sample sign test is one of the common procedures to develop distribution-free inference for a quantile of a population. A basic requirement of this test is that the observations in a sample must be independent. This assumption is violated in certain settings, such as clustered data, grouped data and longitudinal studies. Failure to account for dependence structure leads to erroneous statistical inferences. In this study, we have developed statistical inference for a population quantile of order p in either balanced or unbalanced designs by incorporating dependence structure when the distribution of within-cluster observations is exchangeable. We provide a point estimate, develop a testing procedure and construct confidence intervals for a population quantile of order p. Simulation studies are performed to demonstrate that the confidence intervals achieve their nominal coverage probabilities. We finally apply the proposed procedure to Academic Performance Index data.
- Statistical inference for critical continuous state and continuous time
branching processes with immigration- Abstract: Abstract
We study asymptotic behavior of conditional least squares estimators for critical continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.
PubDate: 2016-04-12
- Abstract: Abstract
We study asymptotic behavior of conditional least squares estimators for critical continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.
- Exceedances of records
- Abstract: Abstract
Given a sequence of random variables (rv’s) and a real function
\(\psi \)
, the
\(\psi \)
-exceedances form a subsequence consisting of those rv’s larger than a function,
\(\psi \)
, of the previous element of the subsequence. We present the basic distribution theory of
\(\psi \)
-exceedances for a sequence of independent and identically distributed rv’s. We give several examples and we study with more detail the case of exponential parents with
\(\psi \)
a linear function. The particular case of arithmetic exceedances is useful to describe the behavior of a type I counter when the arrival process of particles follows a non-homogeneous Poisson process. We also mention applications to destructive testing, early alert systems and the departure process of a
\(M_t/D/1/1\)
queue.
PubDate: 2016-04-12
- Abstract: Abstract
Given a sequence of random variables (rv’s) and a real function
\(\psi \)
, the
\(\psi \)
-exceedances form a subsequence consisting of those rv’s larger than a function,
\(\psi \)
, of the previous element of the subsequence. We present the basic distribution theory of
\(\psi \)
-exceedances for a sequence of independent and identically distributed rv’s. We give several examples and we study with more detail the case of exponential parents with
\(\psi \)
a linear function. The particular case of arithmetic exceedances is useful to describe the behavior of a type I counter when the arrival process of particles follows a non-homogeneous Poisson process. We also mention applications to destructive testing, early alert systems and the departure process of a
\(M_t/D/1/1\)
queue.