Master of Science / Department of Statistics / Haiyan Wang / The purpose of this report is to numerically compare several tests that are applicable to longitudinal data when the experiment contains a large number of treatments or experimental conditions. Such data are increasingly common as technology advances. Of interest is to evaluate if there is any significant main effect of treatment or time, and their interactions. Traditional methods such as linear mixed-effects models (LME), generalized estimating equations (GEE), Wilks' lambda, Hotelling-Lawley, and Pillai's multivariate tests were developed under either parametric distributional assumptions or the assumption of large number of replications. A few recent tests, such as Zhang (2008), Bathke & Harrar (2008), and Bathke & Harrar (2008) were specially developed for the setting of large number of treatments with possibly small replications. In this report, I will present some numerical studies regarding these tests. Performance of these tests will be presented for data generated from several distributions.

The purpose of this research was to evaluate the effect on parametric and nonparametric tests using ordinal data when the distances between points changed on the measurement scale. The research examined the performance of Type I and Type II error rates using selected parametric and nonparametric tests.

The Rasch sampler is an efficient algorithm to sample binary matrices with given marginal sums. It is a Markov chain Monte Carlo (MCMC) algorithm. The program can handle matrices of up to 1024 rows and 64 columns. A special option allows to sample square matrices with given marginals and fixed main diagonal, a problem prominent in social network analysis. In all cases the stationary distribution is uniform. The user has control on the serial dependency. (authors' abstract)

This thesis analyses, derives and evaluates specification tests of Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) regression models, both univariate and multivariate. Of particular interest, in the first half of the thesis, is the derivation of robust test procedures designed to assess the Constant Conditional Correlation (CCC) assumption often employed in multivariate GARCH (MGARCH) models. New asymptotically valid conditional moment tests are proposed which are simple to construct, easily implementable following the full or partial Quasi Maximum Likelihood (QML) estimation and which are robust to non-normality. In doing so, a non-normality robust version of the Tse's (2000) LM test is provided. In addition, a new and easily programmable expressions of the expected Hessian matrix associated with the QMLE is obtained. The finite sample performances of these tests are investigated in an extensive Monte Carlo study, programmed in GAUSS.In the second half of the thesis, attention is devoted to nonparametric testing of GARCH regression models. First simultaneous consistent nonparametric tests of the conditional mean and conditional variance structure of univariate GARCH models are considered. The approach is developed from the Integrated Generalized Spectral (IGS) and Projected Integrated Conditional Moment (PICM) procedures proposed recently by Escanciano (2008 and 2009, respectively) for time series models. Extending Escanciano (2008), a new and simple wild bootstrap procedure is proposed to implement these tests. A Monte Carlo study compares the performance of these nonparametric tests and four parametric tests of nonlinearity and/or asymmetry under a wide range of alternatives. Although the proposed bootstrap scheme does not strictly satisfy the asymptotic requirements, the simulation results demonstrate its ability to control the size extremely well and therefore the power comparison seems justified. Furthermore, this suggests there may exist weaker conditions under which the tests are implementable. The simulation exercise also presents the new evidence of the effect of conditional mean misspecification on various parametric tests of conditional variance. The testing procedures are also illustrated with the help of the S&P 500 data. Finally the PICM and IGS approaches are extended to the MGARCH case. The procedure is illustrated with the help of a bivariate CCC-GARCH model, but can be generalized to other MGARCH specifications. Simulation exercise shows that these tests have satisfactory size and are robust to non-normality. The marginal mean and variance tests have excellent power; however the covariance marginal tests lack power for some alternatives.

This thesis considers the problem of hypothesis testing for umbrella alternatives when there are two groups, or strata, of observations. The proposed methods extend a previously established general framework of hypothesis testing based on rankings to stratified datasets by first aligning the strata. The tests based on the Spearman and Kendall distances between ranking vectors lead to the traditional aligned-rank tests and new methods which account for “misalignment” under the alternative hypothesis. Asymptotic null distributions and simulation studies are given for the Spearman distance. Diagnostic tools for the misalignment issue are illustrated alongside the proposed tests on a dataset of IQ scores of coma patients. Extensions to three or more strata and ”adaptive” tests are provided as future research directions.

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Made available in DSpace on 2015-04-23T12:43:05Z (GMT). No. of bitstreams: 1 larissa.pdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2013-07-23 / Alavancado pelo processo da globalização, a qualidade tornou-se função decisiva para a conquista de clientes e competitividade. Assim, as organizações estão evoluindo para o aperfeiçoamento de seus métodos de gestão, com intuito de atender aos requisitos exigidos pelos clientes. Dentro do contexto da gestão da qualidade, um dos métodos mais difundidos é o Ciclo PDCA, que pode ser desdobrado dentro de cada processo da organização e para o sistema de processos em sua totalidade. No setor de serviços, a percepção do cliente é indispensável para alteração de diretriz de controle (melhorias). Para isto, a estatística pode ser utilizada para viabilizar a coleta, o processamento e a disposição das informações, de forma que o conhecimento gerado é utilizado, por meio do Ciclo PDCA, para atingir metas de melhoria. Neste sentido, o trabalho objetiva propor um modelo de inferência estatística sobre a qualidade do processo de compra pública direta em Instituição de Ensino. Para isso, foi analisada a rotina do setor de compras, na qual se fez o uso das ferramentas da qualidade e dos testes não paramétricos para fazer comparações entre grupos de fatores. Com isso, foi possível identificar os fatores que influenciam de forma significativa o aumento do tempo dos processos. A abordagem da pesquisa é qualitativa, principalmente na coleta e análise dos dados, e quantitativa no tratamento. Quanto aos fins, a natureza da pesquisa é exploratória e descritiva e quanto aos meios de investigação, um estudo de caso. Com base no marco teórico, foi possível elaborar um modelo de procedimentos para execução de uma experimentação que envolve o Ciclo PDCA, as ferramentas da qualidade e os testes não paramétricos para inferência estatística sobre a qualidade do processo. A partir da aplicação deste modelo, identificou-se que o fator valor alto é o mais significativo no processo de compra pública direta. Fora este fator, a natureza do processo classificada como material permanente e processos que tramitam por mais de dezesseis setores também são fatores que influenciam no aumento do tempo. Dessa forma, foi possível contribuir com a área de gestão da qualidade, visto que se delineou a respeito da inferência estatística na qualidade em processos de compras, um assunto pouco difundido no âmbito do setor público.

在試題難易度分析上，傳統方式常以答對率或得分率的高低來認定試題的難易度。但答對率或得分率高低並不能真正表達應試者在答題時的難易感受程度。過去研究指出影響數學科試題難易度的主要因素有三：評量的數學內容、解題時的思考策略及解題所需的步驟數。 本論文針對影響數學科試題難易度的三個主要因素進行分析統計。以模糊統計的角度，提出非固定權重因子之二維模糊數。應用模糊數絕對距離的概念以摒除族群中異端值，最後針對不同族群進行難易指標分析與檢定。 / On the basis of difficulty analysis, the hit rate or the scoring rate are considered as the index of the difficulty of the questions traditionally. However, these rates can not represent how test takers feel when taking tests. According to the previous papers on this subject, they note three factors to affect the difficulty analysis on math questions the content of the evaluation, the strategies of question solving, and the required steps to solve a question. This research is focused on the three major factors which influence the difficulty of math examinations. With the angle of fuzzy statistics, a two-dimension fuzzy number will be presented with non-fixed weighted factors. By applying the absolute distance concept of fuzzy number, the extreme values are excluded. Consequently, the indices of difficulty from different groups can be tested and analyzed.

本文主要的目的是藉由The Geometer's Sketchpad (GSP)軟體的設計，幫助我們得到一組連續型模糊樣本。另外對於模糊數的無母數檢定我們提供了一個較為一般的方法，可以針對梯型、三角型，區間型的模糊樣本同時進行處理。 藉由利用GSP. 軟體所設計的模糊問卷，可以較清楚地紀錄受訪者的感覺，此外我們所提供之對於模糊數的無母數檢定方法比其他方法較為有效力。 在未來的研究裡，我們仍有一些問題需要解決，呈述如下：當所施測的樣本數很大時，如何有效率的在網路上紀錄受測者所建構的隸屬度函數？ / The purpose of this paper is to develop a methodology for getting a continuous fuzzy data by using the software The Geometer's Sketchpad (GSP). And we propose a general method for nonparametric tests with fuzzy data that can deal with trapezoid, triangular, and interval-valued data simultaneously. Using the fuzzy questionnaire designed by GSP. can help respondents to record their thoughts more precisely. Additionally our method for nonparametric tests with fuzzy data is more powerful than others. Additional research issues for further investigation are expressed by question such as follows: how to record the membership function on line, especially when the sample size is large?

Σε αυτήν την έρευνα, κατασκευάσαμε την διορθωμένη για κίνδυνο κατάταξη αποδόσεων για την περίπτωση των ελληνικών μετοχικών αμοιβαίων κεφαλαίων. Η διορθωμένη για κίνδυνο απόδοση μετρά τη ποσότητα του κινδύνου και εκφράζεται γενικά ως αριθμός ή κατάταξη. Οι διορθωμένες για κίνδυνο αποδόσεις εφαρμόζονται σε μεμονωμένα αξιόγραφα, επενδυτικά κεφάλαια και σε χαρτοφυλάκια. Η εμμονή ορίζεται ως ένα φαινόμενο όπου η σχετική (κατάταξη) απόδοση τείνει να επαναλαμβάνεται σε διαδοχικά χρονικά διαστήματα. Εφαρμόσαμε διάφορα τεστ προκειμένου να αξιολογηθεί η παρουσία ή όχι της εμμονής. Τα εμπειρικά αποτελέσματα μας έδειξαν ότι η εμμονή γίνεται πιο αδύναμη σε μακροπρόθεσμο χρονικό ορίζοντα. / In this research we constructed the ranking of the risk adjusted returns in the case of the Greek equity mutual funds market. Risk adjusted returns is a concept that refines an investment's return by measuring how much risk is involved in producing that return, which is generally expressed as a number or rating. Risk-adjusted returns are applied to individual securities and investment funds and portfolios. Persistence is defined as a phenomenon where relative (ranked) performance tends to repeat across successive time intervals. We apply various tests in order to assess the presence or not of persistence. Our analysis documents that persistence becomes weaker as the investment horizon is increased.