An EM algorithm for the estimation of parameters of bivariate generalized exponential distribution under random left censoring

In this paper, we consider the four-parameter bivariate generalized exponential distribution proposed by Kundu and Gupta [Bivariate generalized exponential distribution, J. Multivariate Anal. 100 (2009), pp. 581–593] and propose an expectation–maximization algorithm to find the maximum-likelihood estimators of the four parameters under random left censoring. A numerical experiment is carried out to discuss the properties of the estimators obtained iteratively.     

Non-negative estimation of variance components in heteroscedastic one-way random-effects ANOVA models

There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established.     

Formulas for stationary planar fibre processes III – intersections with fibre systems

In this paper we investigate the distribution of the periodogram, respectively, the periodogram matrix for stationary random sequences. These .distributions are consid¬ered in the case of a fixed frequency as well as in the case of a finite number of frequencies for Gaussian sequences and for sequences of independent random variables. The exact distribution is obtained in the case of a fixed frequence for one-dimensional GAUSsian sequences. Asymptotic expansions, respectively, the rate of convergence to the asymptotic distribution are given in the case mentioned above     

Robust location estimation with missing data

In a missing data setting, we have a sample in which a vector of explanatory variables ${\bf x}_i$ is observed for every subject i, while scalar responses $y_i$ are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L‐functionals and M‐functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived. The proofs of the theorems are presented in Supplementary Material available online. The Canadian Journal of Statistics 41: 111–132; 2013 © 2012 Statistical Society of Canada     

Discrete Multicolour Random Mosaics with an Application to Network Extraction

We introduce a class of random fields that can be understood as discrete versions of multicolour polygonal fields built on regular linear tessellations. We focus first on a subclass of consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation is used to design new sampling techniques for Gibbsian modifications of such fields, a class which covers lattice‐based random fields. A flux‐based modification is applied to the extraction of the field tracks network from a Synthetic Aperture Radar image of a rural area.     

Comparison of Confidence Intervals on Between Group Variance in Unbalanced Heteroscedastic One-Way Random Models

A computer algorithm for computing the alternative distributions of the Wilcoxon signed rank statistic under shift alternatives is discussed. An explicit error bound is derived for the numeric integration approximation to these distributions.

A nonparametric process control procedure in which the standard CUSUM procedure is applied to the Wilcoxon signed rank statistic is discussed. In order to implement this procedure, the distribution of the Wilcoxon statistic under shift of the underlying distribution from its point of symmetry needs to be computed. The average run length of the nonparametric and parametric CUSUM are compared.     

Tests for random time effects and spatial error correlation in panel regression models

We consider a panel model with spatial autocorrelation and heterogeneity across time. Various Lagrange multiplier and likelihood ratio test statistics are developed for testing time effects and spatial effects, jointly, marginally or conditionally. Limiting null distributions of the tests are derived. Size and power performances of the proposed tests are compared by a Monte-Carlo experiment.     

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, the Rosenthal-type maximal inequalities and Kolmogorov-type exponential inequality for negatively superadditive-dependent (NSD) random variables are presented. By using these inequalities, we study the complete convergence for arrays of rowwise NSD random variables. As applications, the Baum–Katz-type result for arrays of rowwise NSD random variables and the complete consistency for the estimator of nonparametric regression model based on NSD errors are obtained. Our results extend and improve the corresponding ones of Chen et al. [On complete convergence for arrays of rowwise negatively associated random variables. Theory Probab Appl. 2007;52(2):393–397] for arrays of rowwise negatively associated random variables to the case of arrays of rowwise NSD random variables.     

Analysis of hybrid censored competing risks data

In this paper, we consider the analysis of hybrid censored competing risks data, based on Cox's latent failure time model assumptions. It is assumed that lifetime distributions of latent causes of failure follow Weibull distribution with the same shape parameter, but different scale parameters. Maximum likelihood estimators (MLEs) of the unknown parameters can be obtained by solving a one-dimensional optimization problem, and we propose a fixed-point type algorithm to solve this optimization problem. Approximate MLEs have been proposed based on Taylor series expansion, and they have explicit expressions. Bayesian inference of the unknown parameters are obtained based on the assumption that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameters have Beta–Gamma priors. We propose to use Markov Chain Monte Carlo samples to compute Bayes estimates and also to construct highest posterior density credible intervals. Monte Carlo simulations are performed to investigate the performances of the different estimators, and two data sets have been analysed for illustrative purposes.     

Random translation of discrete order statistics

We investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose order statistics are related by a random translation. We also provide some examples using the constructive method that we propose.