On some statistical selection procedures

Yuning Liao, Purdue University

Abstract

This thesis deals with some statistical selection and ranking problems. Classical subset selection procedures are modified to incorporate prior information. The performance of these procedures is examined and compared with that of the usual classical procedures. In Chapter 2 and Chapter 3, we investigate the problem of selecting the best unknown mean of several normal populations. We use noninformative prior on the whole real line and the positive real line. Under these assumptions, some interesting results have been derived and discussed. One particular result shows that the bound on the probability of a correct selection P(CS), for the natural subset selection rule of $R\sp{max}$-type can be connected with the size of the selected subset. In Chapter 4, we study the problem of subset selection for the binomial populations based on a class of priors of the unknown parameter associated with the best population. The approach we use includes the classical subset selection procedure as a special case. Optimal choices of the procedures, when the prior information about the largest parameter is known, unknown, or partly known, are investigated. Also, applications to the comparison with a control and Poisson population problems are studied. In Chapter 5, the exact distribution of the sample mean of a double exponential (Laplace) distribution has been derived. A classical subset selection procedure based on the sample mean for selecting the population associated with the largest (smallest) location parameter of k double exponential (Laplace) distributions is proposed and studied. Chapter 6 deals with a confidence lower bound for the probability of a correction selection (PCS) in location parameter models. Practical confidence lower bounds for the PCS in location parameter models are presented with a user's choice of a dimension q ($1\le q\le k-1$) for computation, where k is the number of populations. With an appropriate modification, the result can be applied to location-scale parameter models with an unknown scale parameter.

Degree

Ph.D.

Advisors

Gupta, Purdue University.

Subject Area

Statistics

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