An important problem in statistical inference is to check the adequacy of models upon which inferences are based. Some valuable tools are available for examining a model's suitability of which the most widely used is the goodness-of-fit test. The pioneering work in this area is by Karl Pearson (1900). Since then, a considerable amount of work has been done so far and investigation is still going on in this field due to its importance in the hypothesis testing problem.This thesis contains an expository discussion of the goodness-of-fit tests, intended for the users of the statistical theory. An attempt is made here to give a complete coverage of the historical development, present status and other current problems related to this topic. Numerical examples are provided to best explain the test procedures. The contents, taken as a whole, constitute a unified presentation of some of the most important aspects of goodness-of-fit tests.Ball State UniversityMuncie, IN 57406

The Empirical Likelihood method (ELM) was introduced by A. B. Owen to test hypotheses in the early 1990s. It's a nonparametric method and uses the data directly to do statistical tests and to compute confidence intervals/regions. Because of its distribution free property and generality, it has been studied extensively and employed widely in statistical topics. There are many classical test statistics such as the Cramer-von Mises (CM) test statistic, the Anderson-Darling test statistic, and the Watson test statistic, to name a few. However, none is universally most powerful. This thesis is dedicated to extending the ELM to several interesting statistical topics in hypothesis tests. First of all, we focus on testing the fit of distributions. Based on the CM test, we propose a novel Jackknife Empirical Likelihood test via estimating equations in testing the goodness-of-fit. The proposed new test allows one to add more relevant constraints so as to improve the power. Also, this idea can be generalized to other classical test statistics. Second, when aiming at testing the error distributions generated from a statistical model (e.g., the regression model), we introduce the Jackknife Empirical Likelihood idea to the regression model, and further compute the confidence regions with the merits of distribution free limiting chi-square property. Third, the ELM based on some weighted score equations are proposed for constructing confidence intervals for the coefficient in the simple bilinear model. The effectiveness of all presented methods are demonstrated by some extensive simulation studies.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 159-165). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2004. / Typescript. Vita. Includes bibliographical references (leaves 159-165). Also available on the Internet.

Thesis (Ph. D.)--University of California, San Diego, 2009. / Title from first page of PDF file (viewed August 11, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 134-136).

Thesis (M.S.)--Brigham Young University. Dept. of Statistics, 2006. / Includes bibliographical references (p. 83-85).

Thesis (Ph.D.)--Ohio University, June, 2010. / Title from PDF t.p. Includes bibliographical references.

Thesis (M. A.)--University of Notre Dame, 2005. / Thesis directed by Ke-Hai Yuan for the Department of Psychology. "October 2005." Includes bibliographical references (leaves 60-63).

Thesis (Ph. D.)--University of Notre Dame, 2006. / Thesis directed by George S. Howard for the Department of Psychology. "December 2006." Includes bibliographical references (leaves 49-52).