Merging data from multiple sources: pretest and shrinkage perspectives

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.

KEYWORDS:

• Common mean
• preliminary test estimator
• Stein-type shrinkage estimators
• asymptotic distributional quadratic bias
• asymptotic distributional quadratic risk
• local alternatives

AMS SUBJECT CLASSIFICATION:

• 62F10
• 62F12

Acknowledgments

Thanks are due to an anonymous Associate Editor and reviewers for their valuable comments and suggestions that improved an earlier version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Muhammad Kashif Ali Shah http://orcid.org/0000-0003-1741-3701

Supranee Lisawadi http://orcid.org/0000-0002-3214-4610

Additional information

Funding

The authors gratefully acknowledge the financial support provided by Thammasat University under the TU Research Scholar (Contract No. 51/2559).