Merging data from multiple sources: pretest and shrinkage perspectives. Issue 8 (24th May 2017)

• Record Type: Journal Article
• Authors: Shah, Muhammad Kashif Ali; Lisawadi, Supranee; Ejaz Ahmed, S.
• Is Part Of: Journal of statistical computation and simulation. Volume 87:Issue 8(2017)
• Page Start: 1577
• Page End: 1592
• Publication Date: 2017-05-24
• Subjects: Common mean -- preliminary test estimator -- Stein-type shrinkage estimators -- asymptotic distributional quadratic bias -- asymptotic distributional quadratic risk -- local alternatives; 62F10 -- 62F12; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2016.1277427
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: 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.