Abstract: The class of all bivariate copulas that are invariant under univariate truncation is characterized. To this end, a family of bivariate copulas generated by a real-valued function is introduced. The obtained results are also used in order to show that the Clayton family of copulas (including its limiting elements) coincides with the class of copulas that are invariant under bivariate truncation and contains all exchangeable copulas which are invariant under univariate truncation.

Abstract: Let T be a lifetime random variable. In order to study the properties of T in reliability theory and survival analysis, several measures are proposed in the literature. Among these measures, hazard rate, mean residual lifetime, reversed hazard rate and the mean past lifetime (MPL) play important roles. In the present paper, we focus mainly on the MPL. We investigate its properties in connection with other reliability measures. Some results on partial ordering and characterization are also given. Finally, we deal with its statistical estimation.

Abstract: Reflexive shifting of a given distribution, using its own distribution function, can reveal information. The shifts are changes in measure such that the separation of the resulting left and right unit shifted distributions reveals the binary entropy of position, called locational or partition entropy. This can be used for spread and asymmetry functions. Alternatively, summary metrics for distributional asymmetry and spread can be based on the relative strengths of left- and right-hand shifts. Such metrics are applicable even for long tail densities where distributional moments may not exist.

Abstract: Epstein [Truncated life tests in the exponential case, Ann. Math. Statist. 25 (1954), pp. 555–564] introduced a hybrid censoring scheme (called Type-I hybrid censoring) and Chen and Bhattacharyya [Exact confidence bounds for an exponential parameter under hybrid censoring, Comm. Statist. Theory Methods 17 (1988), pp. 1857–1870] derived the exact distribution of the maximum-likelihood estimator (MLE) of the mean of a scaled exponential distribution based on a Type-I hybrid censored sample. Childs et al. [Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Ann. Inst. Statist. Math. 55 (2003), pp. 319–330] provided an alternate simpler expression for this distribution, and also developed analogous results for another hybrid censoring scheme (called Type-II hybrid censoring). The purpose of this paper is to derive the exact bivariate distribution of the MLE of the parameter vector of a two-parameter exponential model based on hybrid censored sample...

Abstract: We introduce a new tool to investigate some distributional properties of order statistics and records related by a random translation (contraction or dilation) scheme. This technique is based on the property of uniqueness of solutions of certain non-linear integral equations of Volterra type. We show how this tool is used to obtain new characterizations of distributions.

Abstract: In this paper, we establish the risk function of a class of estimator for the mean parameter matrix of a matrix variate normal distribution. In particular, the established result is useful in evaluating the performance of a class of shrinkage-pretest-type estimators.

Abstract: Recently, Liebscher [Construction of asymetric multivariate copulas, J Multivariate Anal 99 (2008), pp 2234–2250] introduced a general construction scheme of d-variate copulas which generalizes the Archimedean family Similarly, Morillas [A method to obtain new copulas from a given one, Metrika 61 (2005), pp 169–184] proposed a method to obtain a variety of new copulas from a given d-copula Both approaches coincide only for the particular subclass of Archimedean copulas Within this work, we present a unifying framework which includes both Liebscher and Morillas copulas as special cases Above that, more general copulas may be constructed First examples are given

Abstract: Earlier researchers have studied some aspects of the classes of distribution functions with decreasing alpha-percentile residual life (DPRL(alpha)), 0 < alpha < 1. The purpose of this paper is to note some further properties of these classes, and to initiate a theory of non-parametric statistical estimation of DPRL(alpha) functions. Specifically, the close relationship between the DPRL(alpha) and the increasing failure rate ageing notions is studied. Other close relationships, between the DPRL(alpha) ageing notions and the percentile residual life stochastic orders, are described, and further properties of the above classes of distributions are derived. Finally, we introduce an estimator of the percentile residual life function, under the condition that it decreases, and we prove its strongly uniform consistency.

Abstract: A representation of the Fisher information in generalized order statistics in terms of the hazard rate of the underlying distribution function is derived under mild regularity conditions. This expression supplements results for complete, Type-II censored, and progressively Type-II censored data. As a byproduct, we find a hazard rate based representation for samples of k-records which apparently has not been known so far. Moreover, sufficient conditions for the validity of this representation in location and scale family settings are given. The result is illustrated by considering generalized order statistics based on logistic, Laplace, and extreme value distributions.

Abstract: We examine the Gaussian quasi-maximum likelihood estimator (QMLE) for random coefficient autoregressions. Consistency and asymptotic normality are established for general random coefficients and general correlation structure between these coefficients and the noise. In particular, the obtained results apply even if the stationary solution has infinite absolute mean or infinite variance. Next an application to the integer-valued times series modelling is given which provides a novel alternative for traditional INAR-like models for these series.

Abstract: Assume that the explanatory variable X is valued in some abstract semi-metric functional space and the response variable Y is real-valued In this paper, we investigate a modified kernel estimation of the regression function r(x)=E(Y|X=x) The main goal of this paper is to establish the consistency and the rate of convergence of such a modified kernel estimator for strong mixing functional data with only E|Y|<∞, which weakens the moment assumption on the response variable Y

Abstract: A trivial projective change of a Finsler metric F is the Finsler metric F + d f. I explain when it is possible to make a given Finsler metric both forward and backward complete by a trivial projective change.Though the problem is purely Finslerian, it was inspired by Lorentz geometry and mathematical relativity: it was observed that it is possible to understand the light-like geodesics of a (normalized, standard) stationary 4-dimensional space time as geodesics of a certain Finsler Randers metric on a 3-dimensional manifold. The trivial projective change of the Finsler metric corresponds to the choice of another 3-dimensional slice, and the existence of a trivial projective change that is forward and backward complete is equivalent to the global hyperbolicity of the space time.

Abstract: In the classical Bootstrap approach the number of distinct observation in the resample is random. To overcome this hitch Rao et al. [Bootstrap by sequential resampling, J. Statist. Plan. Inference 64 (1997), pp. 257–281] have proposed a modified resampling procedure – the so-called Sequential Bootstrap or 0.632-Bootstrap – in which each resample has exactly the same number m ∼eq ⌊0.632 n⌋ of distinct observations. Motivated by this idea we introduce an akin procedure, the Subsample Bootstrap, where additionally even the size of each resample is equal. It will turn out that the Subsample Bootstrap empirical process is consistent for a wide class of Donsker classes.

Abstract: It is important to detect the variance heterogeneity in regression models. Heteroscedasticity tests have been well studied in parametric and nonparametric regression models. This paper presents a consistent test for heteroscedasticity for nonlinear semi-parametric regression models with nonparametric variance function based on the kernel method. The properties of the test are investigated through Monte Carlo simulations. The test methods are illustrated with a real example.

Abstract: For the first time, explicit closed-form expressions are derived for the characteristic functions for the Burr III and Burr XII distributions. The expressions involve the Fox -function and the Wright generalized 2Ψ0-function. An application is illustrated for insurance.

Abstract: This paper is concerned with the problem of obtaining Bayesian prediction bounds of future observables from a finite mixture of Burr type XII distribution with its reciprocal based on type-I censored data. We consider the one-sample and two-sample prediction schemes using the Markov chain Monte Carlo algorithm. Numerical examples are given to illustrate the procedures and the accuracy of prediction intervals is investigated via extensive Monte Carlo simulation.

Abstract: In this paper, we present the asymptotic properties of maximum quasi-likelihood estimators (MQLEs) in generalized linear models with adaptive designs under some mild regular conditions. The existence of MQLEs in quasi-likelihood equation is discussed. The rate of convergence and asymptotic normality of MQLEs are also established. The results are illustrated by Monte-Carlo simulations.

Abstract: In this paper, we introduce a stochastic restricted k–d class estimator for the vector of parameters in a linear model when additional linear restrictions on the parameter vector are assumed to hold. The stochastic restricted k–d class estimator is a generalization of the ordinary mixed estimator and the k–d class estimator. We show that our new biased estimator is superior in the mean squared error matrix sense to the k–d class estimator [S. Sakallioglu and S. Kaciranlar, A new biased estimator based on ridge estimation, Statist. Papers 49 (2008), pp. 669–689] and the stochastic restricted Liu estimator [H. Yang and J.W. Xu, An alternative stochastic restricted Liu estimator in linear regression, Statist. Papers 50 (2009), pp. 639–647]. Finally, a numerical example is given to show the theoretical results.

Abstract: In this paper, we show that the proportions of observations falling in the left and right vicinity of the k n th order statistic converge in probability to some population quantities. We then prove...

Abstract: An unknown moment-determinate cumulative distribution function or its density function can be recovered from corresponding moments and estimated from the empirical moments. This method of estimating an unknown density is natural in certain inverse estimation models like multiplicative censoring or biased sampling when the moments of unobserved distribution can be estimated via the transformed moments of the observed distribution. In this paper, we introduce a new nonparametric estimator of a probability density function defined on the positive real line, motivated by the above. Some fundamental properties of proposed estimator are studied. The comparison with traditional kernel density estimator is discussed.

Abstract: A capture–recapture estimation method for closed wildlife population has been adapted by epidemiologists to estimate the size of a hidden or hard-to-reach population. The heterogeneity of capture probabilities on the estimation of population size using capture–recapture data is considered in this article. A generalized estimating equation approach to the problem of estimating capturing probabilities is presented by considering the heterogeneity of the study population. Resulting probabilities then serve as denominators for calculating the size of the population.

Abstract: In this paper, we consider the preliminary test approach for the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The preliminary test two-parameter estimators based on the Wald (W), likelihood ratio, and Lagrangian multiplier tests are given, when it is suspected that the regression parameter may be restricted to a subspace and the regression error is distributed with multivariate Student's t distribution. The bias and mean square error of the proposed estimators are derived and compared. The conditions of superiority of the proposed estimators are obtained. Finally, we conclude that the optimum choice of the level of significance becomes the traditional choice by using the Wald test.

Abstract: Product moments of bivariate chi-square distribution have been derived in closed forms. Finite expressions have been derived for product moments of integer orders. Marginal and conditional distributions, conditional moments, coefficient of skewness and kurtosis of conditional distribution have also been discussed. Shannon entropy of the distribution is also derived. We also discuss the Bayesian estimation of a parameter of the distribution. Results match with the independent case when the variables are uncorrelated.

Abstract: In this paper, we consider the application of the empirical likelihood method to a partially linear model with measurement errors in the non-parametric part. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Furthermore, we obtain the maximum empirical likelihood estimate of the unknown parameter by using the empirical log-likelihood ratio function, and the resulting estimator is shown to be asymptotically normal. Some simulations and an application are conducted to illustrate the proposed method.

Abstract: Consider the nonparametric regression model with martingale difference errors. Nonparametric estimator g n (x) of regression function g(x) will be introduced, and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of g n (x) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors.

Abstract: In this paper, we suggest three new ratio estimators of the population mean using quartiles of the auxiliary variable when there are missing data from the sample units. The suggested estimators are investigated under the simple random sampling method. We obtain the mean square errors equations for these estimators. The suggested estimators are compared with the sample mean and ratio estimators in the case of missing data. Also, they are compared with estimators in Singh and Horn [Compromised imputation in survey sampling, Metrika 51 (2000), pp. 267–276], Singh and Deo [Imputation by power transformation, Statist. Papers 45 (2003), pp. 555–579], and Kadilar and Cingi [Estimators for the population mean in the case of missing data, Commun. Stat.-Theory Methods, 37 (2008), pp. 2226–2236] and present under which conditions the proposed estimators are more efficient than other estimators. In terms of accuracy and of the coverage of the bootstrap confidence intervals, the suggested estimators performed better t...

Abstract: Laplace gave a divergent expansion for Mills’ ratio. Truncated to k terms, a bound is known for the remainder. We extend this result to repeated integrals of the normal density. Taylor series are also given for these.

Abstract: The paper deals with generalized confidence intervals for the between-group variance in one-way heteroscedastic (unbalanced) ANOVA with random effects. The approach used mimics the standard one applied in mixed linear models with two variance components, where interval estimators are based on a minimal sufficient statistic derived after an initial reduction by the principle of invariance. A minimal sufficient statistic under heteroscedasticity is found to resemble its homoscedastic counterpart and further analogies between heteroscedastic and homoscedastic cases lead us to two classes of fiducial generalized pivots for the between-group variance. The procedures suggested formerly by Wimmer and Witkovský [Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model, J. Stat. Comput. Simul. 73 (2003), pp. 333–346] and Li [Comparison of confidence intervals on between group variance in unbalanced heteroscedastic one-way random models, Comm. Statist. Sim...

Abstract: We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.