Home

# Distribution Theory of Some Nonparametric Statistics via Finite Markov Chain Imbedding Technique

 dc.contributor.supervisor Fu, James C. (Statistics) en_US dc.contributor.author Lee, Wan-Chen dc.date.accessioned 2014-04-16T13:46:22Z dc.date.available 2014-04-16T13:46:22Z dc.date.issued 2014-04-16 dc.identifier.uri http://hdl.handle.net/1993/23513 dc.description.abstract The ranking method used for testing the equivalence of two distributions has been studied for decades and is widely adopted for its simplicity. However, due to the complexity of calculations, the power of the test is either estimated by normal approximation or found when an appropriate alternative is given. Here, via a Finite Markov chain imbedding (FMCI) technique, we are able to establish the marginal and joint distributions of the rank statistics considering the shift and scale parameters, respectively and simultaneously, under two continuous distribution functions. Furthermore, the procedures of distribution equivalence tests and their power functions are discussed. Numerical results of a joint distribution of two rank statistics under the standard normal distribution and the powers for a sequence of alternative normal distributions with mean from -20 to 20 and standard deviation from 1 to 9 and their reciprocals are presented. In addition, we discuss the powers of the rank statistics under the Lehmann alternatives. en_US Wallenstein et. al. (1993, 1994) discussed power via combinatorial calculations for the scan statistic against a pulse alternative; however, unless certain proper conditions are given, computational difficulties exist. Our work extends their results and provides an alternative way to obtain the distribution of a scan statistic under various alternative conditions. An efficient and intuitive expression for the distribution as well as the power of the scan statistic are introduced via the FMCI. The numerical results of the exact power for a discrete scan statistic against various conditions are presented. Powers through the finite Markov chain imbedding method and a combinatorial algorithm for a continuous scan statistic against a pulse alternative of a higher risk for a disease on a specified subinterval time are also discussed and compared. dc.subject FMCI en_US dc.subject hypothesis test en_US dc.subject Lehmann alternative en_US dc.subject rank statistic en_US dc.subject rank-sum test en_US dc.subject scan statistic en_US dc.subject shift parameter en_US dc.subject scale parameter en_US dc.subject power en_US dc.title Distribution Theory of Some Nonparametric Statistics via Finite Markov Chain Imbedding Technique en_US dc.degree.discipline Statistics en_US dc.contributor.examiningcommittee Guo, Benqi (Mathematics) Leblanc, Alexandre (Statistics) Wang, Xikui (Statistics) Li, Deli (Lakehead University) en_US dc.degree.level Doctor of Philosophy (Ph.D.) en_US dc.description.note May 2014 en_US
﻿