Bayesian inference of the inverse Weibull mixture distribution using type-I censoring

A large number of models have been derived from the two-parameter Weibull distribution including the inverse Weibull (IW) model which is found suitable for modeling the complex failure data set. In this paper, we present the Bayesian inference for the mixture of two IW models. For this purpose, the Bayes estimates of the parameters of the mixture model along with their posterior risks using informative as well as the non-informative prior are obtained. These estimates have been attained considering two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. For the former case, Bayes estimates are obtained under three loss functions while for the latter case only the squared error loss function is used. Simulation study is carried out in order to explore numerical aspects of the proposed Bayes estimators. A real-life data set is also presented for both cases, and parameters obtained under case when shape parameter is known are tested through testing of hypothesis procedure.     

Estimation for two-way analysis of variance with correlated errors

We consider some estimation and distribution problems encountered in a two way analysis of variance model with only one observation per cell, errors correlated in one level, and the variances are not necessarily equal. The independence criteria for the row and interaction mean sum of squares and distribution of the maximum likelihood estimator of the correlation coefficient are given.     

Weak convergence of residual median process for dependent or randomly censored samples

This article studies the weak convergence of the residual median process (i) when the observations follow a strictly stationary ø-mixing process and (ii) when hte observations are randomly censored. In both these cased the residual median prodeas converges weakly to a gaussian process.     

On the Stochastic Restricted Almost Unbiased Estimators in Linear Regression Model

In this article, the stochastic restricted almost unbiased ridge regression estimator and stochastic restricted almost unbiased Liu estimator are proposed to overcome the well-known multicollinearity problem in linear regression model. The quadratic bias and mean square error matrix of the proposed estimators are derived and compared. Furthermore, a numerical example and a Monte Carlo simulation are given to illustrate some of the theoretical results.     

Calibrated linear unbiased estimators in finite population sampling

Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38] and Rao [2002. Discussion of “Exact linear unbiased estimation in survey sampling”. J. Stat. Plann. Inf. 102, 39–40] suggested some useful techniques of deriving a linear unbiased estimator of a finite population total by modifying a given linear estimator. In this paper we suggest various generalizations of their results. In particular, we search for estimators satisfying the calibration property with respect to a related auxiliary variable and obtain some new calibrated unbiased ratio-type estimators for arbitrary sampling designs. We also explore a few properties of one of the estimators suggested in Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38].     

Logistic regression analysis of randomized response data with missing covariates

Randomized response is an interview technique designed to eliminate response bias when sensitive questions are asked. In this paper, we present a logistic regression model on randomized response data when the covariates on some subjects are missing at random. In particular, we propose Horvitz and Thompson (1952)-type weighted estimators by using different estimates of the selection probabilities. We present large sample theory for the proposed estimators and show that they are more efficient than the estimator using the true selection probabilities. Simulation results support theoretical analysis. We also illustrate the approach using data from a survey of cable TV.     

The exact density of nonparametric regression estimators: fixed design case

This paper studies the exact density of a general nonparametric regression estimator when the errors are non-normal. The fixed design case is considered. The density function is derived by an application of the technique of Davis (1976)     

Incorporating historical controls using a random-effects model with a normal prior

Employing a variance stabilization transformation, a random-effects model with a normal prior is proposed for incorporating historical controls in the estimation of dose-response relationships. The advantages and disadvantages of maximum likelihood and empirical Bayes estimators are discussed. A two-stage method is introduced for the prudent use of historical controls.     

ON ESTIMATION FOLLOWING SELECTION FROM NONREGULAR DISTRIBUTIONS

Independent random samples are drawn from k (≥ 2) populations, having probability density functions belonging to a general truncation parameter family. The populations associated with the smallest and the largest truncation parameters are called the lower extreme population (LEP) and the upper extreme population (UEP), respectively. For the goal of selecting the LEP (UEP), we consider the natural selection rule, which selects the population corresponding to the smallest (largest) of k maximum likelihood estimates as the LEP (UEP), and study the problem of estimating the truncation parameter of the selected population. We unify some of the existing results, available in the literature for specific distributions, by deriving the uniformly minimum variance unbiased estimator (UMVUE) for the truncation parameter of the selected population. The conditional unbiasedness of the UMVUE is also checked. The cases of the left and the right truncation parameter families are dealt with separately. Finally, we consider an application to the Pareto probability model, where the performances of the UMVUE and three other natural estimators are compared with each other, under the mean squared error criterion.     

Small area estimation of poverty indicators

The authors propose to estimate nonlinear small area population parameters by using the empirical Bayes (best) method, based on a nested error model. They focus on poverty indicators as particular nonlinear parameters of interest, but the proposed methodology is applicable to general nonlinear parameters. They use a parametric bootstrap method to estimate the mean squared error of the empirical best estimators. They also study small sample properties of these estimators by model‐based and design‐based simulation studies. Results show large reductions in mean squared error relative to direct area‐specific estimators and other estimators obtained by “simulated” censuses. The authors also apply the proposed method to estimate poverty incidences and poverty gaps in Spanish provinces by gender with mean squared errors estimated by the mentioned parametric bootstrap method. For the Spanish data, results show a significant reduction in coefficient of variation of the proposed empirical best estimators over direct estimators for practically all domains. The Canadian Journal of Statistics 38: 369–385; 2010 © 2010 Statistical Society of Canada