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The simultaneous estimation of Cronbachs alpha coefficients from q populations under the compound symmetry assumption is considered. In a multi-sample scenario, it is suspected that all the Cronbac...

In this article, we have developed asymptotic theory for the simultaneous estimation of the k means of arbitrary populations under the common mean hypothesis and further assuming that corresponding population variances are unknown and unequal. The unrestricted estimator, the Graybill-Deal-type restricted estimator, the preliminary test, and the Stein-type shrinkage estimators are suggested. A large sample test statistic is also proposed as a pretest for testing the common mean hypothesis. Under the sequence of local alternatives and squared error loss, we have compared the asymptotic properties of the estimators by means of asymptotic distributional quadratic bias and risk. Comprehensive Monte-Carlo simulation experiments were conducted to study the relative risk performance of the estimators with reference to the unrestricted estimator in finite samples. Two real-data examples are also furnished to illustrate the application of the suggested estimation strategies.

In this article, a large sample pooling procedure is considered for the reliability function of a Weibull distribution. Asymptotic properties of shrinkage estimation procedures based on the preliminary test are developed. It is shown that the proposed estimator has substantially smaller asymptoticmean squared error (AMSE) than the usual maximumlikelihood (ML) estimator inmost of the parameter space. Analytic AMSE expressions of the proposed estimators are obtained and the dominance picture of the estimators is presented by comparing them. It is shown that the suggested estimators yield a wider dominance range over theML estimator than the usual pretest estimator and give a meaningful size of the pretest. To appraise the small sample performance of the estimators, detailed Monte-Carlo simulation studies are also carried out.

Under the homogeneity assumption of k reliability functions from a two-parameter Weibull distribution, we have developed the asymptotic theory for the simultaneous estimation of reliability functions. Improved estimation strategies based on the Graybill Deal, preliminary test and the James-Stein type shrinkage principles are discussed. Using the sequence of local alternatives and squared error loss function, we have derived the asymptotic distributional quadratic bias and risk of the said estimators. A comparison in terms of risk has also been carried out among the listed estimators relative to the benchmark maximum likelihood estimator. To be more specific, we have pointed out the regions where our suggested estimators perform better than other estimators. A comprehensive Monte-Carlo simulation study is presented to validate the behavior of various estimation methods in terms of simulated relative efficiency along with a real-data application.

This article addresses the problem of parameter estimation of the logistic regression model under subspace information via linear shrinkage, pretest, and shrinkage pretest estimators along with the traditional unrestricted maximum likelihood estimator and restricted estimator. We developed an asymptotic theory for the linear shrinkage and pretest estimators and compared their relative performance using the notion of asymptotic distributional bias and asymptotic quadratic risk. The analytical results demonstrated that the proposed estimation strategies outperformed the classical estimation strategies in a meaningful parameter space. Detailed Monte-Carlo simulation studies were conducted for different combinations and the performance of each estimation method was evaluated in terms of simulated relative efficiency. The results of the simulation study were in strong agreement with the asymptotic analytical findings. Two real-data examples are also given to appraise the performance of the estimators.