Typescript (photocopy). / Digitized by Kansas Correctional Industries

Thesis (Ph.D.) -- University of Texas at Arlington, 2009.

Thesis--Wisconsin. / Vita. Includes bibliographical references (leaves 65-68).

University of Macau / Faculty of Science and Technology / Department of Civil and Environmental Engineering

Nonparametric tests have served as robust alternatives to traditional statistical tests with rigid underlying assumptions. If a researcher expects the treatment effects to follow an umbrella alternative, then the test developed in this research will be applicable in the Balanced Incomplete Block Design (Hemmer’s test). It is hypothesized that Hemmer’s test will prove to be more powerful than the Durbin test when the umbrella alternative is true. A mixed design consisting of a Balanced Incomplete Block Design and a Randomized Complete Block Design will also be considered, where two additional test statistics are developed for the umbrella alternative. Monte Carlo simulation studies were conducted using SAS to estimate powers. Various underlying distributions were used with 3, 4, and 5 treatments, and a variety of peaks and mean parameter values. For the mixed design, different ratios of complete to incomplete blocks were considered. Recommendations are given.

published_or_final_version / Statistics / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

The problem considered relates to estimating an arbitrary regression function m(x) from sample pairs (Xᵢ,Yᵢ) 1 ≤ i ≤ n. A model is assumed of the form Y = m(x) + ε(x) where ε(x) is a random variable with expectation 0. One well known method for estimating m(x) is by using one of a class of kernel regression estimators say m(n)(x). Schuster (1972) has shown conditions under which the limiting distribution of the kernel estimator m(n)(x) is the normal distribution. It might also be of interest to use the data to estimate the distribution of m(n)(x). One could, given this estimate, construct approximate confidence bounds for the function m(x). Three estimators are proposed for the density of m(n)(x). They share a basis in non-parametric kernel regression and utilize bootstrap techniques to obtain the density estimate. The order of convergence of one of the estimators is examined and conditions are given under which the order is higher then when estimation is by the normal approximation. Finally the performance of each estimator for constructing confidence bounds is compared for moderate sample sizes using computer studies.

Wenyang Zhang. / "October 1998." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 190-196). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

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