Inferential Methods for Extreme Value Regression Models

Abstract

<p>In this thesis, we consider different inferntial methods for the multi-group extreme value regression model and evaluate their relative merits.</p> <p>First, we derive expressions of estimators of the parameters for the multi-group extreme value regression model using the following methods: (i) best linear unbiased estimation (BLUE), (ii) maximum likelihood estimation (MLE), (iii) approximate maximum likelihood estimation (AMLE), and (iv) large-sample approximation to the best linear unbiased estimation. These derivations are presented for complete samples, progessively Type-II right-censored samples, and its special case - Type-II right-censored samples. Explicit expressions of the estimators' bias (for AMLE), asymptotic (or approximate) variances and covariances are derived as well, for all the methods mentioned above. A proof of the asymptotic normality of the BLUE's of the parameters for the multi-group extreme value regression model is presented. We then compare these estimation methods for various choices of samples sizes and censoring schemes through a Monte Carlo simulation study.</p> <p>We also study the confidence interval estimation of these parameters through pivotal quantities and simulate the probablility coverages of confidence intervals based on all the methods for various choices of sample sizes and censoring schemes. A comparision of these probability coverages is made as well, and some conclusions are drawn.</p> <p>We illustrate all these inferential methods through three real-life examples discuessed earlier by Lawless (1982).</p> <p>Finally in order to test the validity of the assumption of the extreme regression model, we extend Tiku and Singh's (1981) method to the multi-group extreme value regression model. We determine the level of significance as well as the power under different alternatives for various choices of sample sizes and censoring schemes through Monte Carlo simulations.</p>