Date Available
5-4-2011
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.
Recommended Citation
Barton, William H., "COMPARISON OF TWO SAMPLES BY A NONPARAMETRIC LIKELIHOOD-RATIO TEST" (2010). University of Kentucky Doctoral Dissertations. 99.
https://uknowledge.uky.edu/gradschool_diss/99
