S. E. Ahmed

Shrinkage Estimation of Regression Coefficients From Censored Data With Multiple Observations

This paper considers the preliminary test and Stein-type estimation of regression parameters in exponential regression failure time distribution. We consider a situation where the lifetime data may be right censored with multiple observations taken at each regression vector. We propose improved estimators of the regression vector when it is suspected that the true regression parameter vectors may be restricted to a linear subspace. The large sample risk properties of the proposed estimators are derived. The relative merits of the proposed estimators are discussed.

Risk comparison of some shrinkage M-estimators in linear models

The problem of robust estimation of a (linear) regression parameter (vector), in the presence of nuisance scale parameter, is considered when it is a priori suspected that the regression could be restricted to a linear subspace. Asymptotic properties of variants of Stein-rule M-estimators (including the positive-rule shrinkage M-estimators) are studied. Under an asymptotic distributional quadratic risk criterion, their relative dominance picture is explored, analytically as well as by simulation. An extensive sampling experiment is used to examine the small sample characteristics of the proposed estimators over a wide-range of data sampling designs and distributions. Our simulation experiments have provided strong evidence that corroborates with the asymptotic theory. Two examples are provided to illustrate the performance of the estimators in real-life situations.

Shrinkage preliminary test estimation in multivariate normal distributions

To estimate the mean vector of a multivariate normal distribution , a random sample of size n 1is used. Suppose a second independent random sample of size n 2from is available and it is a priori suspected that μ (1) = μ (2) may hold. We propose a shrinkage preliminary test estimate (SPTE) mean vector μ (1) that may be viewed as a preliminary test estimator improving the usual one given by Ahmed (1987). This proposed estimator is superior in bias and efficiency to the usual preliminary test estimator (PTE). Furthermore, it dominates the classical estimator in a range that is wider than that of the usual preliminary estimator. The size of the preliminary test for SPTE is much more appropriate .than the PTE.

Estimation strategies for the intercept vector in a simple linear multivariate normal regression model

Abstract For a simple multivariate regression model, the problem of estimating the intercept vector is considered when it is apriori suspected that the slope may be restricted to a subspace. Four estimation strategies have been developed for the intercept parameter. In this situation, the estimates based on a preliminary test as well as on the Stein-rule are desirable. Exact bias and risks of all of these estimators are derived and their efficiencies relative to classical estimators are studied under quadratic loss function. An optimum rule for the preliminary test estimator is discussed. It is shown that the shrinkage estimator dominates the classical one, whereas none of the preliminary test and shrinkage estimator dominate each other. It is found that shrinkage estimator dominates the preliminary test estimator except in a range around the restriction. Further, for large values of α, the level of statistical significance, shrinkage estimator dominates the preliminary test estimator uniformly.

To pool or not to pool: The discrete data

The purpose of this paper is to discuss the classical problem of pooling proportions of two independent random samples taken from two possibly identical binomial distributions. The primary interest is in the estimation of [theta]1 from population I. Three estimators, i.e. the classical estimator, pooled estimator and preliminary test estimator are proposed. Their asymptotic mean squared errors are derived and compared.

Pooling multivariate data

In case it is doubtful whether two sets of data have the same mean vector, four estimation strategies have been developed for the target mean vector. In this situation, the estimates based on a preliminary test as well as on Stein-rule are advantageous. Two measures of relative efficiency are considered; one based on thequadratic loss function, and the other on the determinant of the mean square error matrix. A max-min rule for the size of the preliminary test of significance is presented. It is demonstrated that the shrinkage estimator dominates the classical estimator, whereas none of the shrinkage estimator and the preliminary test estimator dominate each other. The range in the parameter space where preliminary test estimator dominates shrinkage is investigated analytically and computationally. It is found that the shrinkage estimator outperform the preliminary test estimator except in a region around the null hypothesis. Moreover, for large values of a, the level of statistical significance, shrinkag...

Biased estimation in a simple multivariate regression model

Abstract Estimation of the intercept vector in a simple multivariate normal regression model is considered, when it is a priori suspected that the slope vector may be restricted to a subspace. We propose two new Stein-type and preliminary test estimators for the parameter vector. The positive-part estimator is superior to the usual Stein-type estimator, and the proposed preliminary test estimator outperforms the standard preliminary test estimator regardless of the correctness of the nonsample information. The relative dominance picture of estimators is presented.

Improved Estimation of Coefficient Vector in a Regression Model

Abstract In this article we consider the problem of estimating the coefficient vector of a classical regression model when it is apriori suspected that the parameters vector may belong to a subspace. Two estimators; namely the positive-part of Stein-type estimator and the improved preliminary test estimator are proposed and it is demonstrated analytically as well as numerically that the proposed estimators dominate the usual Stein-type and pretest estimators respectively. The proposed estimators are also compared in terms of risks with that of the unrestricted estimator and we find that the positive-part of Stein-type estimator uniformly dominates the unrestricted estimator while the improved preliminary test estimator dominates the unrestricted estimator in a wider range than that of the usual pretest estimator.

Simultaneous Estimation of Several Intraclass Correlation Coefficients

Based on shrinkage and preliminary test rules, various estimators are proposed for estimation of several intraclass correlation coefficients when independent samples are drawn from multivariate normal populations. It is demonstrated that the James-Stein type estimators are asymptotically superior to the usual estimators. Furthermore, it is also indicated through asymptotic results that none of the preliminary test and shrinkage estimators dominate each other, though they perform relatively well as compared to the classical estimator. The relative dominance picture of the estimators is presented. A Monte Carlo study is performed to appraise the properties of the proposed estimators for small samples.

Inference concerning quantile for left truncated and right censored data

The problem of both testing and estimating the quantile function when the data are left truncated and right censored (LTRC) is considered. The aim of this communication is two-fold. First, a large sample test statistic to test for the quantile function under the LTRC model is defined and its null and non-null distributions are derived. A Monte Carlo simulation study is conducted to assess the power of the proposed test statistic that is used to define the estimators. Secondly, an improved estimation of the quantile function is investigated. In the spirit of the shrinkage principle in parameter estimation, three estimators assuming an uncertain prior non-sample information on the value of the quantile are proposed. The asymptotic bias and mean square error of the estimators are derived and compared with the usual estimator. The method is illustrated with hypothetical data as well as real data.