Estimation Of Variance In Bivariate Normal Distribution After Preliminary Test Of Homogeneity

Author

Juan Manuel Romero Padilla

Graduation Semester and Year

2014

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Chien-Pai Han

Abstract

A preliminary test estimator of variance in the bivariate normal distribution is proposed after Pitman-Morgan test of homogeneity of two variances. We propose one estimator of variance after preliminary test of two tails and another one for one tail test. The biases and mean square errors of both estimators are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max-min criterion.

Disciplines

Mathematics | Physical Sciences and Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Romero Padilla, Juan Manuel, "Estimation Of Variance In Bivariate Normal Distribution After Preliminary Test Of Homogeneity" (2014). Mathematics Dissertations. 134.
https://mavmatrix.uta.edu/math_dissertations/134