Lichun Wang

Empirical Likelihood in a Semi-Parametric Model for Missing Response Data

Let Y be a response and, given covariate X,Y has a conditional density f(y | x, θ), where θ is a unknown p-dimensional vector of parameters and the marginal distribution of X is unknown. When responses are missing at random, with auxiliary information and imputation, we define an adjusted empirical log-likelihood ratio for the mean of Y and obtain its asymptotic distribution. A simulation study is conducted to compare the adjusted empirical log-likelihood and the normal approximation method in terms of coverage accuracies.

Empirical likelihood for parametric model under imputation for missing data

Abstract In the present paper, we study the empirical likelihood method for a parametric model which parameterizes the conditional density of a response given covariate. It is shown the adjusted empirical log-likelihood ratio is asymptotically standard χ 2 when missing responses are imputed using maximum likelihood estimate.

Linear Bayes estimator for the two-parameter exponential family under type II censoring

For the two-parameter exponential family, a linear Bayes method is proposed to simultaneously estimate the parameter vector consisting of location and scale parameters. The superiority of the proposed linear Bayes estimator (LBE) over the classical UMVUE is established in terms of the mean square error matrix (MSEM) criterion. The proposed LBE is simple and easy to use compared with the usual Bayes estimator, which is obtained by the MCMC method. Numerical results are presented to verify that the LBE works well. In the empirical Bayes framework, the paper invokes a linear empirical Bayes estimator (LEBE) by using a linear combination of historical samples. It is shown under some mild regularity conditions that the LEBE is superior to the classical UMVUE and the maximum likelihood estimator in terms of MSEM. It is further shown with numerical results that the performance of LEBE gets better with the increase in the number of historical samples.

The life-span prediction of a system connected in series

This article considers the prediction problem of the life-span of a system whose components connected in series and the lifetime of the components follows the exponential distribution with probability density f ( x ; ? ) = ? - 1 exp ? ( - x / ? ) I ( x 0 ) . Employing the Bayes method, a prior distribution G ( ? ) is used to describe the variability of ? but the form of G ( ? ) is not specified and only one moment condition is assumed. Suppose the observed lifetimes of components are rightly censored, we define a prediction statistic to predict the life-span of the series-wound system which consists of some untested components, firstly, under the condition that the censoring distribution is known and secondly, that it is unknown. For several different priors, we investigate the coverage frequencies of the proposed prediction intervals as the sample size and the censorship proportion change. The simulation study shows that our predictions are efficient and applicable.

On estimating uniform distribution via linear Bayes method

ABSTRACT A linear Bayes procedure is suggested to simultaneously estimate the parameters of the uniform distribution U(θ1, θ2). The proposed linear Bayes estimator is simple and easy to use and its superiorities are established.

Consistency of Posterior Distributions for Heteroscedastic Nonparametric Regression Models

In this article, we consider Bayesian inferences for the heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown. We demonstrated consistency of posterior distributions for this model using priors induced by B-splines expansion, treating both random and deterministic covariates in a uniform manner.

Life prediction under random censorship

Based on censored samples, this paper proposes a statistic to predict the average value of some future samples which denotes the average life of the second round sampling. Differing from the usual Bayesian prediction, we do not specify the prior distribution of the parameter, and only some moment conditions are assumed. Simulation studies are conducted to investigate the prediction results.

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.