Abstract: Abstract
The strong consistency of the least squares estimator in multiple regression models is established assuming the randomness of the regressors and errors with infinite variance. Only moderately restrictive conditions are imposed on the stochastic model matrix and the errors will be random variables having moment of order
$r,\,1 \leqslant r \leqslant 2$
. In our treatment, we use Etemadi’s strong law of large numbers and a sharp almost sure convergence for randomly weighted sums of random elements. Both techniques permit us to extend the results of some previous papers. PubDate: 2013-05-05
Abstract: Abstract
In the two-sample prediction problem, record values from the present sample may be used as predictors of order statistics from a future sample. In this paper, we investigate the nearness of record statistics (upper and lower) to order statistics from a location-scale family of distributions in the sense of Pitman closeness and discuss the corresponding monotonicity properties. We then determine the closest record value to a specific order statistic from a future sample. Even though in general it depends on the parent distribution, exact and explicit expressions are derived for the required probabilities in the case of exponential and uniform distributions, and some computational results are presented as well. Finally, we consider the mean squared error criterion and examine the corresponding results in the exponential case. PubDate: 2013-05-01
Abstract: Abstract
In this paper we study convolution residuals, that is, if
$X_1,X_2,\ldots ,X_n$
are independent random variables, we study the distributions, and the properties, of the sums
$\sum _{i=1}^lX_i-t$
given that
$\sum _{i=1}^kX_i>t$
, where
$t\in \mathbb R $
, and
$1\le k\le l\le n$
. Various stochastic orders, among convolution residuals based on observations from either one or two samples, are derived. As a consequence computable bounds on the survival functions and on the expected values of convolution residuals are obtained. Some applications in reliability theory and queueing theory are described. PubDate: 2013-05-01
Abstract: Abstract
Given a large sample from a location-scale population we estimate the unknown parameters by means of confidence regions constructed on the basis of two order statistics. The problem of the best choice of those statistics to obtain good estimates, as
$n\rightarrow \infty ,$
is considered. PubDate: 2013-05-01
Abstract: Abstract
Capture–Recapture methods aim to estimate the size of an elusive target population. Each member of the target population carries a count of identifications by some identifying mechanism—the number of times it has been identified during the observational period. Only positive counts are observed and inference needs to be based on the observed count distribution. A widely used assumption for the count distribution is a Poisson mixture. If the mixing distribution can be described by an exponential density, the geometric distribution arises as the marginal. This note discusses population size estimation on the basis of the zero-truncated geometric (a geometric again itself). In addition, population heterogeneity is considered for the geometric. Chao’s estimator is developed for the mixture of geometric distributions and provides a lower bound estimator which is valid under arbitrary mixing on the parameter of the geometric. However, Chao’s estimator is also known for its relatively large variance (if compared to the maximum likelihood estimator). Another estimator based on a censored geometric likelihood is suggested which uses the entire sample information but is less affected by model misspecifications. Simulation studies illustrate that the proposed censored estimator comprises a good compromise between the maximum likelihood estimator and Chao’s estimator, e.g. between efficiency and bias. PubDate: 2013-05-01
Abstract: Abstract
In this paper, we propose a test on the parametric form of the coefficient functions in the varying coefficient model with missing response. Two groups of completed data sets are constructed by using imputation and inverse probability weighting methods respectively. By noting that the coefficient part can be a regression function for a specific model, we construct two empirical process-based tests. The asymptotical distributions of the proposed tests under null and local alternative hypothesis are investigated respectively. Simulation study is carried out to show the power performance of the test. We illustrate the proposed approaches with an environmental data set. PubDate: 2013-05-01
Abstract: Abstract
This paper considers the optimal design problem for multiresponse regression models. The
$R$
-optimality introduced by Dette (J R Stat Soc B 59:97–110, 1997) for single response experiments is extended to the case of multiresponse parameter estimation. A general equivalence theorem for the
$R$
-optimality is provided for multiresponse models. Illustrative examples of the
$R$
-optimal designs for two multiresponse models are presented based on the general equivalence theorem. PubDate: 2013-05-01
Abstract: Abstract
In this paper, we discuss discrete compound distributions, in which the counting distribution is a weighted Poisson distribution. The over- and under-dispersion of these distributions are then discussed by analyzing the Fisher index of dispersion as well as a newly introduced factorial moment to mean measure. Several cases of compounding distributions and weight functions are subsequently examined in detail. PubDate: 2013-05-01
Abstract: Abstract
Let
$\{W_m\}{_{m\ge 1}}$
be the sequence of weak records from a discrete parent random variable,
$X$
, supported on the non-negative integers. We obtain a new characterization of geometric distributions based on an additive property of weak records:
$X$
follows a geometric distribution if and only if for certain integers,
$n,\, s\ge 1, W_{n+s}\stackrel{d}{=}W_n+W^{\prime }_s$
, with
$W^{\prime }_s$
independent of
$W_n$
and
$W^{\prime }_s\stackrel{d}{=} W_s$
. PubDate: 2013-05-01
Abstract: Abstract
Motivated by the effect hierarchy principle, Zhang et al. (Stat Sinica 18:1689–1705, 2008) introduced an aliased effect number pattern (AENP) for regular fractional factorial designs and based on the new pattern proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal
$2^{n-m}$
designs. Zhang et al. (Stat Sinica 18:1689–1705, 2008) proved that most existing criteria can be obtained by functions of the AENP. In this paper we propose a simple method for the calculation of AENP. The method is much easier than before since the calculation only makes use of the design matrix. All 128-run GMC designs with the number of factors ranging from 8 to 32 are provided for practical use. PubDate: 2013-04-20
Abstract: Abstract
We consider estimation of the mean vector,
$\theta $
, of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non decreasing Laplacian of the form
$\pi (\Vert \theta \Vert ^{2})$
, under certain conditions on the generating function
$f(\cdot )$
of the sampling distributions. The class of sampling distributions includes certain variance mixtures of normals. PubDate: 2013-04-11
Abstract: Abstract
This paper considers two classes of bivariate distributions having proportional (reversed) hazard rates models as their marginals. Various dependence properties of the proposed models are studied through their copulas. PubDate: 2013-04-09
Abstract: Abstract
This paper considers estimation of a functional partially quantile regression model whose parameters include the infinite dimensional function as well as the slope parameters. We show asymptotical normality of the estimator of the finite dimensional parameter, and derive the rate of convergence of the estimator of the infinite dimensional slope function. In addition, we show the rate of the mean squared prediction error for the proposed estimator. A simulation study is provided to illustrate the numerical performance of the resulting estimators. PubDate: 2013-04-09
Abstract: Abstract
In this paper, we investigate the effect of a single cold standby component on the performance of a coherent system. In particular, we focus on coherent systems which may fail at the time of the first component failure in the system. We obtain signature based expressions for the survival function and mean time to failure of the coherent systems satisfying the abovementioned property. PubDate: 2013-04-06
Abstract: Abstract
In this paper, we discuss interval estimation for the common mean of several heterogeneous log-normal (LN) populations. The proposed procedure is based on a higher order likelihood method. The merits of our proposed method are numerically compared with other three methods with respect to their expected lengths and coverage probabilities. Numerical studies have shown that the coverage probabilities of the proposed method are very accurate even for very small samples. The methods are also illustrated with an example. PubDate: 2013-04-01
Abstract: Abstract
Two methods are given for adapting a kernel density estimate to obtain an estimate of a density function with bias O(h
p
) for any given p, where h = h(n) is the bandwidth and n is the sample size. The first method is standard. The second method is new and involves use of Bell polynomials. The second method is shown to yield smaller biases and smaller mean squared errors than classical kernel density estimates and those due to Jones et al. (Biometrika 82:327–338, 1995). PubDate: 2013-04-01
Abstract: Abstract
Considering the presence of first order residual effects of treatments, a family of variance balanced changeover designs has been presented and universal optimality of the designs is established. The designs use only v experimental units and (v − 1)/2 periods for v = 4t + 3 prime or prime power number of treatments; t being a positive integer. A special feature of the proposed designs is that ‘in the order of presentation of treatments to experimental units over periods, each treatment is once immediately preceded by only half of the other treatments and is immediately followed once by the remaining half of the treatments’. This characteristic results in reducing the size of the variance balanced designs considerably. PubDate: 2013-04-01
Abstract: Abstract
In this paper, we consider the estimation problem of individual weights of three objects. For the estimation we use the chemical balance weighing design and the criterion of D-optimality. We assume that the error terms
${\varepsilon_{i},\ i=1,2,\dots,n,}$
are a first-order autoregressive process. This assumption implies that the covariance matrix of errors depends on the known parameter ρ. We present the chemical balance weighing design matrix
${\widetilde{\bf X}}$
and we prove that this design is D-optimal in certain classes of designs for
${\rho\in[0,1)}$
and it is also D-optimal in the class of designs with the design matrix
${{\bf X} \in M_{n\times 3}(\pm 1)}$
for some ρ ≥ 0. We prove also the necessary and sufficient conditions under which the design is D-optimal in the class of designs
${M_{n\times 3}(\pm 1)}$
, if
${\rho\in[0,1/(n-2))}$
. We present also the matrix of the D-optimal factorial design with 3 two-level factors. PubDate: 2013-04-01
Abstract: Abstract
The main result of the paper is the following characterization of the generalized arcsine density p
γ
(t) = t
γ−1(1 − t)
γ−1/B(γ, γ) with
${t \in (0, 1)}$
and
${\gamma \in(0,\frac12) \cup (\frac12,1)}$
: a r.v. ξ supported on [0, 1] has the generalized arcsine density p
γ
(t) if and only if
${ {\mathbb E} \xi- x ^{1-2 \gamma}}$
has the same value for almost all
${x \in (0,1)}$
. Moreover, the measure with density p
γ
(t) is a unique minimizer (in the space of all probability measures μ supported on (0, 1)) of the double expectation
${ (\gamma-\frac12 ) {\mathbb E} \xi-\xi^{\prime} ^{1-2 \gamma}}$
, where ξ and ξ′ are independent random variables distributed according to the measure μ. These results extend recent results characterizing the standard arcsine density (the case
${\gamma=\frac12}$
). PubDate: 2013-04-01
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