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In this paper, we derive the asymptotic distribution of the Augmented Dickey-Fuller t Test statistics, t_{ADF}, against a generalized fractional integrated process (for example: ARFIMA(p,1+d,q) ,|d|<1/2,and p, q be positive integer) by using the propositions of Lee and Shie (2003). Then we discuss why the power decreases with the increasing lags in the same and large enough sample size T when d is unequal to 0. We also get that the estimator of the disturbance's variance, S^2, has slightly increasing bias with increasing k. Finally, we support the conclusion by the Monte Carlo experiments.

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Houdre, Christian; Committee Member: Bakhtin, Yuri; Committee Member: Foley, Robert; Committee Member: Koltchinskii, Vladimir; Committee Member: Lifshitz, Mikhail; Committee Member: Matzinger, Heinrich; Committee Member: Popescu, Ionel. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures. This powerful framework contains most of the published procedures in this area as special cases, such as maximally selected chi-squared and rank statistics, but also allows for direct construction of new test procedures for less standard test problems. As an application, a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions. This new test is employed to search for a high-risk group of rectal cancer patients treated with a neo-adjuvant chemoradiotherapy. Moreover, a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints. / Series: Research Report Series / Department of Statistics and Mathematics

The supLM test for structural change is embedded into a permutation test framework for a simple location model. The resulting conditional permutation distribution is compared to the usual (unconditional) asymptotic distribution, showing that the power of the test can be clearly improved in small samples. Furthermore, generalizations are discussed for binary and multivariate dependent variables as well as model-based permutation testing for structural change. The procedures suggested are illustrated using both artificial and real-world data (number of youth homicides, employment discrimination data, structural-change publications, and stock returns). / Series: Research Report Series / Department of Statistics and Mathematics

Chau Ka Pik. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Maximum Probability Estimator --- p.1 / Chapter 1.2 --- An Outline of the Thesis --- p.4 / Chapter 2 --- Asymptotic Distribution Theory --- p.7 / Chapter 3 --- Exponential Family Noise --- p.16 / Chapter 3.1 --- Stationary Case --- p.16 / Chapter 3.2 --- Nonstationary Case --- p.25 / Chapter 4 --- Conclusions --- p.37 / Bibliography --- p.39

In Bayesian analysis, means are commonly used to summarize Bayesian posterior distributions. Problems with a large number of parameters often require numerical integrations over many dimensions to obtain means. In this dissertation, posterior modes with respect to appropriate measures are used to summarize Bayesian posterior distributions, using the Newton-Raphson method to locate modes. Further inference of modes relies on the normal approximation, using asymptotic multivariate normal distributions to approximate posterior distributions. These techniques are applied to two statistical estimation problems. First, Bayesian sequential dose selection procedures are developed for Bioassay problems using Ramsey's prior [28]. Two adaptive designs for Bayesian sequential dose selection and estimation of the potency curve are given. The relative efficiency is used to compare the adaptive methods with other non-Bayesian methods (Spearman-Karber, up-and-down, and Robbins-Monro) for estimating the ED50 . Second, posterior distributions of the order of an autoregressive (AR) model are determined following Robb's method (1980). Wolfer's sunspot data is used as an example to compare the estimating results with FPE, AIC, BIC, and CIC methods. Both Robb's method and the normal approximation for estimation of the order have full posterior results. / Graduation date: 1992

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 61-64). Also available on the Internet.

Thesis supervisor: Qihe Tang. Includes bibliographic references (p. 111-116).

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 61-64). Also available on the Internet.