Author

Jeong-Ae Kim

Date of Award

8-2004

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Supervisor

Prof. N. Balakrishnan

Abstract

In this thesis, we consider inferential methods for a bivariate normal distribution based on Type-II right censored or progressively Type-II right censored data. We first propose the use of the Expectation-Maximization (EM) algorithm to determine maximum likelihood estimates (MLEs) based on Type-II right censored samples. We derive the asymptotic variances and covariances of the MLEs from the Fisher information (FI) matrix as well as from the partially observed information (POI) matrix by using the missing information principle. There are slight differences between the variances and covariances of the MLEs from the FI matrix and those from the POI matrix, but the advantage of the use of the POI matrix is that it does not require any extensive numerical integration as the FI requires. Next, we derive the MLEs and the asymptotic variance- ovariance matrix of the MLEs based on progressively Type-II right censored samples. To improve the coverage probabilities of the asymptotic confidence intervals (CIs) using the asymptotic normality of the MLEs, especially for the correlation coefficient, we propose to use sample-based Monte Carlo percentage points and the coverage probabilities of the CIs so obtained turn out to be closer to the nominal level. Next, we extend the use of the EM-algorithm to determine MLEs based on progressively Type-II right censored bivariate normal data, and derive the symptotic variances and covariances of the MLEs by using the missing information principle. We discuss the determination of optimal censoring schemes with respect to minimum trace as well as maximum information about p. Type-n right censoring is not to be recommended in general, and that the progressive censoring scheme (n - m, 0, ... ,0) is nearly as efficient as the best progressive censoring scheme for each combination of nand m considered. Finally, we propose three run-based and two rank-based nonparametric tests for independence between life-times and covariates from censored bivariate normal samples. The two rank-based test and the T test based on the sample correlation coefficient perform better (in terms of power) than the three run-based tests under bivariate normality. However, the R tests are robust (in terms of level of significance) when the samples come from a population with heavier tails than the normal distribution, such as the t distribution and the scale- utlier model.

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Mathematics Commons

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