Alternative covariance estimates in a replicated measurement error model with correlated,heteroscedastic errors

The article concerns covariance estimates in a replicated measurement error model with correlated, heteroscedastic errors. Freedman has conjectured that using more of the data will improve estimates of covariance matrices and result in a more efficient estimate of the coefficient of the regression model. The paper confirms the conjecture asymptotically for the case that all random variables are normally distributed, but the gain is not substantial.     

On L 1-consistency of kernel-type density estimator for stationary markov processes

A convergence result for kernel type density estimators, proved by Devroye and Gyrofi (1985), is extended to stationary Markov processess satisfying (G ₂-condition introduced by Rosenblatt (1970).     

Estimation of the location and scale parameters of the extreme value distmbution based on multiply type-II censored samples

In this paper, we consider the problem of estimating the location and scale parameters of an extreme value distribution based on multiply Type-II censored samples. We first describe the best linear unbiased estimators and the maximum likelihood estimators of these parameters. After observing that the best linear unbiased estimators need the construction of some tables for its coefficients and that the maximum likelihood estimators do not exist in an explicit algebraic form and hence need to be found by numerical methods, we develop approximate maximum likelihood estimators by appropriately approximating the likelihood equations. In addition to being simple explicit estimators, these estimators turn out to be nearly as efficient as the best linear unbiased estimators and the maximum likelihood estimators. Next, we derive the asymptotic variances and covariance of these estimators in terms of the first two single moments and the product moments of order statistics from the standard extreme value distribution. Finally, we present an example in order to illustrate all the methods of estimation of parameters discussed in this paper.     

Inflated modified power series distributions with applications

In certain applications involving discrete data, it is sometimes found that X = 0 is observed with a frequency significantly higher than predicted by the assumed model. Zero inflated Poisson, binomial and negative binomial models have been employed in some clinical trials and in some regression analysis problems.

In this paper, we study the zero inflated modified power series distributions (IMPSD) which include among others the generalized Poisson and the generalized negative binomial distributions and hence the Poisson, binomial and negative binomial distributions. The structural properties along with the distribution of the sum of independent IMPSD variables are studied. The maximum likelihood estimation of the parameters of the model is examined and the variance-covariance matrix of the estimators is obtained. Finally, examples are presented for the generalized Poisson distribution to illustrate the results.     

Convergence rates for empirical bayes estimators of parameters in multi-parameter exponential families

This paper obtains the convergence rates of the empirical Bayes estimators of parameters in the multi-parameter exponential families. The rates can approximate to 0(n=¹) arbitrarily. The paper presents the multivariate orthogonal polynomials which are continuous on the total space R^p.     

Smoothing techniques via the bezier curve

Although the Bezier curve is very popular in the area of computational graphics it has rarely been used by statisticians. In this paper we develop methods and techniques for use of the Bezier curve in estimation of density and regression function. Also, asymptotic mean integrated square error for both estimators are derived. Comparisons with kernel estimator are conducted using simulation.     

One-Sided Estimating and Testing Problems for Scale Models from Grouped Samples

Abstract

This article mainly analyzes estimating and testing problems for scale models from grouped samples. Suppose the support region of a density function, which does not depend on parameters, is divided into some disjoint intervals, grouped samples are the number of observations falling in each intervals respectively. The studying of grouped samples may be dated back to the beginning of the century, in which only one sample location and/or scale models is considered. (Shi, N.-Z., Gao, W., Zhang, B.-X. (2001 Shi, N.-Z., Gao, W. and Zhang, B.-X. 2001. One-sided estimating and testing problems for location models from grouped samples. Comm. Statist.—Simul. Comput, 30(4): 895–898.  [Google Scholar]). One-sided estimating and testing problems for location models from grouped samples. Comm. Statist.—Simul. Comput. 30(4)) had investigated one-sided problems for location models, this article discusses one-sided estimating and testing problems for scale models. Some algorithms for obtaining the maximum likelihood estimates of the parameters subject to order restrictions are proposed.     

Estimation of the association for bivariate doubly censored data

We study the problem of estimating the association between two related survival variables when they follow a copula model and the bivariate doubly censored data is available. A two-stage estimation procedure is proposed and the asymptotic properties of the proposed estimator are established. Simulation studies are conducted to investigate the finite sample properties of the proposed estimate.     

Estimation of covariance matrices based on hierarchical inverse-Wishart priors

This paper focuses on Bayesian shrinkage methods for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the conditions for the existence of the posterior distributions. Advantages in terms of numerical simulations of posteriors are shown. A simulation study illustrates the performance of the estimation procedures under three loss functions for relevant sample sizes and various covariance structures.     

Maximum likelihood estimation of parameter structures for the Wishart distribution using constraints

Maximum likelihood estimation under constraints for estimation in the Wishart class of distributions, is considered. It provides a unified approach to estimation in a variety of problems concerning covariance matrices. Virtually all covariance structures can be translated to constraints on the covariances. This includes covariance matrices with given structure such as linearly patterned covariance matrices, covariance matrices with zeros, independent covariance matrices and structurally dependent covariance matrices. The methodology followed in this paper provides a useful and simple approach to directly obtain the exact maximum likelihood estimates. These maximum likelihood estimates are obtained via an estimation procedure for the exponential class using constraints.