A nonparametric test for the interval-censored failure time data is proposed in determining whether p lifetime populations come from the same distribution. For the comparison problem based on interval-censored failure time data, Sun proposed some nonparametric test procedures in recent year. In this paper, we present simulation procedures to verify the test proposed by Sun. The simulation results indicate that the proposed test is not approximately Chisquare distribution with degrees of freedom p-1 but Chisquare distribution with degrees of freedom p-1 times a constant.

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Thesis (M. Sc.)--University of Alberta, 2009. / Title from pdf file main screen (viewed on Dec. 11, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Statistics, Department of Mathematical and Statistical Sciences, University of Alberta." Includes bibliographical references.

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Differential item functioning (DIF) can occur across age, gender, ethnic, and/or linguistic groups of examinee populations. Therefore, whenever there is more than one group of examinees involved in a test, a possibility of DIF exists. It is important to detect items with DIF with accurate and powerful statistical methods. While finding a proper DIP method is essential, until now most of the available methods have been dominated by applications to large scale testing contexts. Since the early 1990s, Ramsay has developed a nonparametric item response methodology and computer software, TestGraf (Ramsay, 2000). The nonparametric item response theory (IRT) method requires fewer examinees and items than other item response theory methods and was also designed to detect DIF. However, nonparametric IRT's Type I error rate for DIF detection had not been investigated. The present study investigated the Type I error rate of the nonparametric IRT DIF detection method, when applied to moderate-to-small-scale testing context wherein there were 500 or fewer examinees in a group. In addition, the Mantel-Haenszel (MH) DIF detection method was included. A three-parameter logistic item response model was used to generate data for the two population groups. Each population corresponded to a test of 40 items. Item statistics for the first 34 non-DIF items were randomly chosen from the mathematics test of the 1999 TEVISS (Third International Mathematics and Science Study) for grade eight, whereas item statistics for the last six studied items were adopted from the DIF items used in the study of Muniz, Hambleton, and Xing (2001). These six items were the focus of this study.

<p>In this thesis, we develop some Bayesian mixture density estimation for univariate and multivariate data. We start proposing a repulsive process favoring mixture components further apart. While conducting inferences on the cluster-specific parameters, current frequentist and Bayesian methods often encounter problems when clusters are placed too close together to be scientifically meaningful. Current Bayesian practice generates component-specific parameters independently from a common prior, which tends to favor similar components and often leads to substantial probability assigned to redundant components that are not needed to fit the data. As an alternative, we propose to generate components from a repulsive process, which leads to fewer, better separated and more interpretable clusters. </p><p>In the second part of the thesis, we face the problem of modeling the conditional distribution of a response variable given a high dimensional vector of predictors potentially concentrated near a lower dimensional subspace or manifold. In many settings it is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiresolution model that scales efficiently to massive numbers of features, and can be implemented efficiently with slice sampling.</p><p> In the third part of the thesis, we deal with the problem of characterizing the conditional density of a multivariate vector of response given a potentially high dimensional vector of predictors. The proposed model flexibly characterizes the density of the response variable by hierarchically coupling a collection of factor models, each one defined on a different scale of resolution. As it is illustrated in Chapter 4, our proposed method achieves good predictive performance compared to competitive models while efficiently scaling to high dimensional predictors.</p> / Dissertation

This thesis examines a newly proposed density estimator in order to evaluate its usefulness for government crop insurance programs confronted by the problem of adverse selection. While the Federal Crop Insurance Corporation (FCIC) offers multiple insurance programs including Group Risk Plan (GRP), what is needed is a more accurate method of estimating actuarially fair premium rates in order to eliminate adverse selection. The Empirical Bayes Nonparametric Kernel Density Estimator (EBNKDE) showed a substantial efficiency gain in estimating crop yield densities. The objective of this research was to apply EBNKDE empirically by means of a simulated game wherein I assumed the role of a private insurance company in order to test for profit gains from the greater efficiency and accuracy promised by using EBNKDE. Employing EBNKDE as well as parametric and nonparametric methods, premium insurance rates for 97 Illinois counties for the years 1991 to 2010 were estimated using corn yield data from 1955 to 2010 taken from the National Agricultural Statistics Service (NASS). The results of this research revealed substantial efficiency gain from using EBNKDE as opposed to other estimators such as Normal, Weibull, and Kernel Density Estimator (KDE). Still, further research using other crops yield data from other states will provide greater insight into EBNKDE and its performance in other situations.

This thesis proposed two nonparametric statistical tests, based on the Kolmogorov-Smirnov distance and L2 mallows disatnce. To implement the proposed tests, nonparametric bootstrap method is employed to approximate the distributions of the test statistics to construct the corresponding bootstrap confidence interval procedures. Monte-Carlo simulations are performed to investigate the actual type I error of the proposed bootstrap procedures. It is found that the type I error of the bootstrap BC confidence interval procedure is close to the nominal level when censoring is not heavy and the boosttrap percentile confidence interval procedure works well when Kolmogorov-Smirnov distance is used to characterize the equivalence. When the data is heavily censored, the procedures based on the Kolmogorov-Smirnov distance have very conservative type I errors, while the procedures based on the Mallows distance are very liberal. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2007-08-01 10:43:32.345

Treatment–covariate interaction is often used in clinical trials to assess the homogeneity of treatment effects over these subgroups defined by a baseline covariate, which is frequently conducted after primary analysis including all patients is completed. When the endpoint is the time to an event, as in the cancer clinical trials, the Cox proportional hazard model with an interaction term has been used exclusively to test the significance of treatment-covariate interaction in oncology literature. But the proportional hazards assumption may not be satisfied by the data from clinical trials. Although there are several procedures proposed in statistical literature to assess the interaction based on a nonparametric measure of interaction or nonparametric models, some of these procedures do not take into the account of the nature of the data well, while some are very complicated which may have limited their applications in practice. In this thesis, a non-parametric procedure based on the smoothed estimate of Patel–Hoel measure is first derived to test the interaction between the treatment and a binary covariate with censored data. The theoretical distribution of the test statistic of the proposed procedure is derived. The proposed procedure is also evaluated through Monte-Carlo simulations and applications to data from a cancer clinical trial. Jackknifed versions of two test statistics based on nonparametric models are then derived by simplifying these test statistics and applying the jackknife method to estimate their variances. These jackknifed tests are also compared with the smoothed test and other related tests. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2011-09-27 11:09:28.449