This dissertation is concerned with the estimation of error variances in a non-replicated two-way classification and with inferences based on the estimators so derived. The postulated model used throughout the present work is / y(,ij) = (mu)(,i) + (beta)(,j) + (epsilon)(,ij), / where y(,ij) is the observation in the i('th) row and j('th) column, (mu)(,i) is the parameter representing the mean of the i('th) row, (beta)(,j) is the parameter representing the additional effect of the j('th) column, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / and the (epsilon)(,ij) are independent, zero-mean, normal variates with / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / A set of unbiased estimates / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / developed in earlier work by Grubbs (J. AMER. STATIST. ASSOC. 43 (1948), 243-264), Ehrenberg (BIOMETRIKA 37 (1950), 347-357) and Russell and Bradley (BIOMETRIKA 45 (1958), 111-129) are considered. / The exact joint density of Q(,1), ..., Q(,r) is obtained for r = 3 and two exact results are derived for testing the null hypothesis, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / unknown, versus the two specific alternatives, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / for at least some j, j = 1, 2, 3, and, / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / Source: Dissertation Abstracts International, Volume: 43-07, Section: B, page: 2258. / Thesis (Ph.D.)--The Florida State University, 1982. / These results are consistent with those obtained by Russell and Bradley. / The exact density is derived for the case where r = 4 and n = 4, but no further exact results are obtained. For r = 4 and general n, an approximate test is obtained for testing / unknown, versus / Interesting results regarding the characteristic function of some quadratic forms closely related to Q(,1), ..., Q(,r) are also presented. It is possible to transform the characteristic function in order to obtain the density, and for r = 3 and n = 4, this density is shown to be identical to the density obtained previously for r = 3.

Let {X(,n), n (GREATERTHEQ) 1} be a sequence of i.i.d. random variables withE(X(,1)) = 0, Var(X(,1)) = 1. Let (psi)(s) be the cumulant generating function (c.g.f.) and / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / be the large deviation rate of X(,1). Let S(,n) = X(,1) + ... + X(,n). Under some mild conditions on (psi), Richter (Theory Prob. Appl. (1957) 2, 206-219) showed that the probability density function f(,n) of(' )S(,n)/SQRT.(n has the asymptotic expression / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / whenever x(,n) = o(SQRT.(n) and SQRT.(n x(,n) > 1. In this dissertation we obtain similar large deviation local limit theorems for arbitrary sequences of random variables, not necessarily sums of i.i.d. random variables, thereby increasing the applicability of Richter's theorem. Let {T(,n), n (GREATERTHEQ) 1} be an arbitrary sequence of non-lattice random variables with characteristic function (c.f.) (phi)(,n). Let (psi)(,n), (gamma)(,n) be the c.g.f. and the large deviation rate of T(,n)/n. The main theorem in Chapter II shows that under some standard conditions on (psi)(,n), which imply that T(,n)/n converges to a constant in probability, the density function K(,n) of T(,n)/n has the asymptotic expression / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / where m(,n) is any sequence of real numbers and (tau)(,n) is defined by(psi)(,n)'((tau)(,n)) = m(,n). When T(,n) is the sum of n i.i.d. random variables our result reduces to Richter's theorem. Similar theorems for lattice valued random variables are also presented which are useful in obtaining asymptotic probabilities for Wilcoxon signed-rank test statistic and Kendall's tau. / In Chapter III we use the results of Chapter II to obtain central limit theorem for sums of a triangular array of dependent random variables X(,j)('(n)), j = 1, ..., n with joint distribution given by z(,n)('-1)exp{-H(,n)(x(,1), ..., x(,n))}(PI)dP(x(,j)), where x(,i) (ELEM) R (FOR ALL) i (GREATERTHEQ) 1. The function H(,n)(x(,1), ..., x(,n)) is known as the Hamiltonian. Here P is a probability measure on R. When H(,n)(x(,1), ..., x(,n)) = -log (phi)(,n)(s(,n)/n), where s(,n) = x(,1) + ... + x(,n) and the probability measure P satisfies appropriate conditions, we show that there exists an integer r (GREATERTHEQ) 1 and a sequence (tau)(,n) such that (S(,n) - n(tau)(,n))/n('1- 1/2r) has a limiting distribution which is non-Gaussian if r (GREATERTHEQ) 2. This result generalizes the theorems of Jong-Woo Jeon (Ph.D. Thesis, Dept. of Stat., F.S.U. (1979)) and Ellis and Newman (Z. Wahrscheinlichkeitstheorie und Verw. Gebiete. (1978) 44, 117-139). Chapters IV and V extend the above to the multivariate case. / Source: Dissertation Abstracts International, Volume: 43-08, Section: B, page: 2615. / Thesis (Ph.D.)--The Florida State University, 1982.

In this essay we present analysis examining the basic dietary structure and its relationship to mortality in the first National Health and Nutrition Examination Survey (NHANES I) conducted between 1971 and 1975. We used results from 24-hour recalls on 10,483 individuals in this study. All of the indivduals in the analytic sample were followed through 1992 for vital status. The mean follow-up period for the participants was 16 years. During follow-up 2,042 (48%) males and 1,754 (27%) females died. We first attempted to capture the inherent structure of the dietary data using principal components analyses (PCA). We performed this estimation separately for each race (white and black) and gender (male and female) and compared the estimated principal components among these four strata. We found that the principal components were similar (but not identical) in the four strata. we also related our estimated principal components to mortality using Cox Proportional Hazards (CPH) models and related dietary component to mortality using forward variable selection. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / July 13, 2015. / Includes bibliographical references. / Dan McGee, Professor Directing Dissertation; Cathy Levenson, University Representative; Xufeng Niu, Committee Member; Debajyoti Sinha, Committee Member.

The ready availability of public-use data from various large national complex surveys has immense potential for the assessment of population characteristics--means, proportions, totals, etcetera. Using a model-based approach, complex surveys can be used to evaluate the effectiveness of treatments and to identify risk factors for important diseases such as cancer. Existing statistical methods based on estimating equations and/or utilizing resampling methods are often not valid with survey data due to design features such as stratification, multistage sampling and unequal selection probabilities. In this paper, we accommodate these design features in the analysis of highly skewed response variables arising from large complex surveys. Specifically, we propose a double-transform-both-sides based estimating equations approach to estimate the median regression parameters of the highly skewed response; the double-transform-both-sides method applies the same transformation twice to both the response and regression function. The usual sandwich variance estimate can be used in our approach, whereas a resampling approach would be needed for a pseudo-likelihood based on minimizing absolute deviations. Furthermore, the double-transform-both-sides estimator is relatively robust to the true underlying distribution, and has much smaller mean square error than the least absolute deviations estimator. The method is motivated by an analysis of laboratory data on urinary iodine concentration from the National Health and Nutrition Examination Survey. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / August 10, 2015. / complex survey, double-transform-both-sides regression, median regression, quantile regression / Includes bibliographical references. / Debajyoti Sinha, Professor Co-Directing Dissertation; Stuart R. Lipsitz, Professor Co-Directing Dissertation; Elwood Carlson, University Representative; Elizabeth Slate, Committee Member; Fred Huffer, Committee Member.

Gene-expression data profile are widely used in all kinds of biomedical studies especially in cancer research. This dissertation work focus on solving the problem of how to combine datasets arising from different studies. Of particular interest is how to remove platform effect alone. The matched sample based cross-platform normalization method we developed are designed to tackle data merging problem in two scenarios: The first is affy-agilent cross-platform normalization which are belong to classic microarray gene expression profile. The second is the integration of microarray data with Next Generation Sequencing genome data. We use several general validation measures to assess and compare with the popular Distance-weighted discrimination method. With the public web-based tool NCI-60 CellMiner and The Cancer Genome Atlas data portal supported, our proposed method outperformed DWD in both cross-platform scenarios. It can be further assessed by the ability of exploring biological features in the studies of cancer type discrimination. We applied our method onto two classification problem: One is Breast cancer tumor/normal status classification on microarray and next generation sequencing datasets; The other is Breast cancer patients chemotherapy response classification on GPL96 and GPL570 microarray datasets. Both problems show the classification power are increased after our matched sample based cross-platform normalization method. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2015. / September 1, 2015. / Includes bibliographical references. / Jinfeng Zhang, Professor Directing Dissertation; Qing-Xiang (Amy) Sang, University Representative; Wei Wu, Committee Member; Xufeng Niu, Committee Member.

To identify influential effects in unreplicated (possibly fractionated) factorial experiments, the effect-sparsity assumption (Box and Meyer (1986), Technometrics 28. 11-18) has been adopted in many studies. Although this assumption has been traditionally used for outlier-detecting problems, it may not be suitable to describe the effects from factorial experiments. In this research, we examine the effect-sparsity approach and propose empirical Bayes methods relaxing this assumption. The study also examines the identification of influential effects based on information about the design structure such as the alias relationships, design resolution, and sizes of interactions. A simulation study, based primarily on the criterion of reducing experimental cost of misidentifying factors, has been performed to compare different methods. The results show that when the number of factors is large and when the factorial experiment is highly fractionated, the incorporation of information about the design structure into the analysis reduces the cost in a screening experiment compared to methods not considering design structure. / Source: Dissertation Abstracts International, Volume: 55-04, Section: B, page: 1504. / Major Professor: Duane A. Meeter. / Thesis (Ph.D.)--The Florida State University, 1994.

Many methods for generating variates from discrete distributions have been developed over the past years. They vary from simple to complicated, from specific to general. Some are based on interesting underlying theory, while others are more concerned with efficient computer implementation. / This dissertation is directed toward the latter. We describe methods that are best suited for efficient (fast) computer implementation. We develop specific programs for both the Poisson and the binomial distributions with two versions of each, one for when the parameters are fixed and the other for when the parameters change from call to call. These programs are developed with a spare-no-expense attitude, and timing comparisons will support our belief that they are faster than any other published methods. / For the fixed-parameter case, an algorithm which combines the table look-up, the square histogram (Marsaglia's lecture notes), and the direct search method is given. We will apply the algorithm to the Poisson and the binomial distributions. / For the variable-parameter Poisson case, we take advantage of Marsaglia's (1986) approach and incorporate additional techniques in order to have a Poisson variate generator which works for any value of $\lambda$, using, most of the time, the integer part of a polynomial in a normal variate. We extend the procedure to the binomial distribution. / Source: Dissertation Abstracts International, Volume: 54-07, Section: B, page: 3697. / Major Professor: George Marsaglia. / Thesis (Ph.D.)--The Florida State University, 1993.

We present a preliminary test for nonlinear structure in large data sets. This procedure consists of transforming the data to remove the correlations, then discretizing the data and finally, studying the cell counts in the resulting contingency table. Formal tests can be performed using the usual chi-squared test statistic; there are several forms of this test depending on the transformations and the discretizing schemes. We derive the limiting joint distribution of the cell counts and the limiting distribution of the chi-squared statistic in various situations, and derive the exact first two moments of the chi-squared test statistic in one situation. We also present simulation results for the limiting distribution of the chi-squared statistic via quantile-quantile plots and then present several examples from both simulated and real data sets. / Source: Dissertation Abstracts International, Volume: 53-10, Section: B, page: 5282. / Major Professor: Fred Huffer. / Thesis (Ph.D.)--The Florida State University, 1992.

It has been almost sixty years since Kolmogorov introduced a distribution-free test for the simple null hypothesis that a distribution function coincides with a given distribution function. In 1949 Doob observed that Kolmogorov's approach could be simplified by transforming the empirical process to an empirical process based on uniform random variables. In recent years this approach has led to the construction of distribution-free tests when unknown parameters are present. The purpose of this dissertation is to apply the transformation approach in the setting of survival analysis, where censoring and covariate information further complicate the problem. Asymptotic distribution-free tests are developed for testing independence of a survival time from a covariate, and for checking the adequacy of Cox's proportional hazards model. The test statistics are obtained from certain test statistic processes (indexed by time and covariate) which converge in distribution to Brownian sheets. A simulation study is carried out to investigate the finite sample properties of the proposed tests and they are applied to data from the British Medical Research Council's (1984) 4th myelomatosis trial. / Source: Dissertation Abstracts International, Volume: 53-11, Section: B, page: 5805. / Major Professor: Ian McKeague. / Thesis (Ph.D.)--The Florida State University, 1992.

The purpose of this study was to provide an exposition on multilevel logistic regression. Included in the study was a description of a two-level logistic-model and a comparison between the two-level logistic model and traditional logistic regression. A strategy for building and analyzing multilevel logistic models was devised and offered in the study, and the modeling strategy was illustrated in the analysis of high school drop-outs. The illustration demonstrated the flexibility and utility of the multilevel model in analyzing the impact of school characteristics on students' decisions to leave school. / Source: Dissertation Abstracts International, Volume: 54-02, Section: B, page: 0921. / Major Professor: F. Craig Johnson. / Thesis (Ph.D.)--The Florida State University, 1993.