Year of Publication

2010

Degree Name

Doctor of Philosophy (PhD)

Document Type

Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Mai Zhou

Abstract

In this dissertation we present a novel computational method, as well as its software implementation, to compare two samples by a nonparametric likelihood-ratio test. The basis of the comparison is a mean-type hypothesis. The software is written in the R-language [4]. The two samples are assumed to be independent. Their distributions, which are assumed to be unknown, may be discrete or continuous. The samples may be uncensored, right-censored, left-censored, or doubly-censored. Two software programs are offered. The first program covers the case of a single mean-type hypothesis. The second program covers the case of multiple mean-type hypotheses. For the first program, an approximate p-value for the single hypothesis is calculated, based on the premise that -2log-likelihood-ratio is asymptotically distributed as ­­χ2(1). For the second program, an approximate p-value for the p hypotheses is calculated, based on the premise that -2log-likelihood-ratio is asymptotically distributed as ­χ2(p). In addition we present a proof relating to use of a hazard-type hypothesis as the basis of comparison. We show that -2log-likelihood-ratio is asymptotically distributed as ­­χ2(1) for this hypothesis. The R programs we have developed can be downloaded free-of-charge on the internet at the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org, package name emplik2. The R-language itself is also available free-of-charge at the same site.

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