Because of the measuring instrument or the biological variability, many studies with survival data involve covariates which are subject to measurement error. In such cases, the naive estimates are usually biased. In this thesis, we propose a bias corrected estimate of the regression parameter for the multinomial probit regression model with covariate measurement error. Our method handles the case when the response variable is subject to interval censoring, a frequent occurrence in many medical and health studies where patients are followed periodically. A sandwich estimator for the variance is also proposed. Our procedure can be generalized to general measurement error distribution as long as the first four moments of the measurement error are known. The results of extensive simulations show that our approach is very effective in eliminating the bias when the measurement error is not too large relative to the error term of the regression model. / Censoring is an intrinsic part in survival analysis. In this thesis, we establish the asymptotic properties of MMLE to general transformation models when data is subject to right or left censoring. We show that MMLE is not only consistent and asymptotically normal, but also asymptotically efficient. Thus our asymptotic results give a definite answer to a long-term argument on the efficiency of the maximum marginal likelihood estimator. The difficulty in establishing these results comes from the fact that the score function derived from the marginal likelihood does not have ordinary independence or martingale structure. We will develop a discretization method in establishing our results. As a special case, our results imply the consistency, asymptotic normality and efficiency for the multinomial probit regression, a popular alternative to the Cox regression model. / General transformation model is an important family of semiparametric models in survival analysis which generalizes the linear transformation model. It not only includes typical Cox regression model, proportional odds model and multinomial probit regression model, but also includes heteroscedastic hazard regression model, general heteroscedastic rank regression model and frailty model. By maximizing the marginal likelihood, a parameter estimation (MMLE) can be obtained with the property that it avoids estimating the baseline survival function and censoring distribution, and such property is enjoyed by the Cox regression model. In this thesis, we study three areas of generalization of general transformation models: main response variable is subject to censoring, covariates are time-varying and covariates are subject to measurement error. / In medical studies, the covariates are not always the same during the whole period of study. Covariates may change at certain time points. For example, at the beginning, n patients accept drug A as treatment. After certain percentage of patients have died, the investigator might add new drug B to the rest of the patients. This corresponds to the case of time-varying covariates. In this thesis, we propose an estimation procedure for the parameters in general transformation model with this type of time-varying covariates. The results of extensive simulations show that our approach works well. / Wu, Yueqin. / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3589. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 74-78). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

General transformation models are a class of semiparametric survival models. The models generalize simple transformation models with more flexibility in modeling data coming from statistical practice. The models include many popular survival models as their special cases, e.g., proportional hazard Cox regression models, proportional odds models, generalized probit models, frailty survival models and heteroscedastic hazard regression models etc. Although the maximum marginal likelihood estimate of parameters in general transformation models with interval censored data is very satisfactory, its large sample properties are open. In this thesis, we will consider the problem and use discretization technique to establish the large sample properties of maximum marginal likelihood estimates with interval censored data. / In general, to reduce possible model bias, many covariates will be collected into a model. Hence a high-dimensional regression model is built. But at the same time, some non-significant variables may be also included in. So one of tasks to build an efficient survival model is to select significant variables. In this thesis, we will focus on the variable selection for general transformation models with ranking data, right censored data and interval censored data. Ranking data are widely seen in epidemiological studies, population pharmacokinetics and economics. Right censored data are the most common data in clinical trials. Interval censored data are another type common data in medical studies, financial, epidemiological, demographical and sociological studies. For example, a patient visits a doctor with a prespecified schedule. In his last visit, the doctor did not find occurrence of an interested event but at the current visit, the doctor found the event has occurred. Then the exact occurrence time of this event was censored in an interval bracketed by the two consecutive visiting dates. Based on rank-based penalized log-marginal likelihood approach, we will propose an uniform variable selection procedure for all three types of data mentioned above. In the penalized marginal likelihood function, we will consider non-concave and Adaptive-LASSO (ALASSO) penalties. For the non-concave penalties, we will adopt HARD thresholding, SCAD and LASSO penalties. ALASSO is an extended version of LASSO. The key of ALASSO is that it can assign weights to effects adaptively according to the importance of corresponding covariates. Therefore it has received more attention recently. By incorporating Monte Carlo Markov Chain stochastic approximation (MCMC-SA) algorithm, we also propose an uniform algorithm to find the rank-based penalized maximum marginal likelihood estimates. Based on the numeric approximation for marginal likelihood function, we propose two evaluation criteria---approximated GCV and BIC---to select proper tuning parameters. Using the procedure, we not only can select important variables but also be able to estimate corresponding effects simultaneously. An advantage of the proposed procedure is that it is baseline-free and censoring-distribution-free. With some regular conditions and proper penalties, we can establish the n -consistency and oracle properties of penalized maximum marginal likelihood estimates. We illustrate our proposed procedure by some simulations studies and some real data examples. At last, we will extend the procedures to analyze stratified survival data. / Keywords: General transformation models; Marginal likelihood; Ranking data; Right censored data; Interval censored data; Variable selection; HARD; SCAD; LASSO; ALASSO; Consistency; Oracle. / Li, Jianbo. / Adviser: Minggao Gu. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 104-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In this thesis, we also investigated various conversion techniques concerning how to improve the performance of multiplierless fast 1-D DCT, and row column 2-D DCT fast algorithms. We have explored a number of choices of conversion techniques having an impact on the performance of multiplierless fast DCT algorithms. Based on our analytical analysis, and experiment results, we have the following findings: (1) a transform based on a reversible inverse generally performs better than a version based on a traditional inverse; (2) a transform with a delayed uniform normalization step can achieve a much better performance; (3) a lifting structure transform can usually achieve better performance than its non-lifting structure version; (4) using an optimized configuration of non-zero digits to approximate the coefficients can help to achieve a much better performance than using a non-optimized configuration. / This thesis proposes effective methods to convert fast DCT algorithms, including 1-D DCT, row column 2-D DCT, and direct 2-D DCT, into their multiplierless versions. The basic conversion techniques used include: (1) to convert any butterfly structures in a DCT algorithm into lifting steps; (2) to use an optimized configuration of non-zero digits to approximate the coefficients so that multiplications can be converted into shift and add operations. We devised an effective algorithm based on the remainder theorem for finding an MSD representation, with minimum wordlength, of any float constant. As the approximation errors of different coefficients often affect the MSE of an approximated fast DCT algorithm differently, we developed an efficient search algorithm for finding an optimized configuration of non-zero digits for approximating each of the coefficients with an appropriate number of non-zero signed digits so that the approximated algorithm could achieve a minimum MSE. / When compared to those multiplierless fast 1-D DCT algorithms developed by others, the multiplierless 1-D DCT fast algorithms developed via our proposed conversion method can achieve similar or better performance in terms of MSE and PSNR. While the published methods were use to approximate only the kernels of the 1-D DCT fast algorithms with butterfly structures, our proposed methods can approximate both the kernels and the normalization steps of any 1-D DCT, row column 2-D DCT, and direct 2-D DCT fast algorithms. / Chan, Kwong Wing Raymond. / "February 2007." / Adviser: Lee Moon Chuen. / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6172. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 110-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Akademische Abhandlung--Helsinki. / Includes bibliographical references (p. [38]).

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2005. / Includes bibliographical references. Also available in electronic version.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

The problem of determining the structure of linear transformations on the algebra of n-square matrices over the complex field is discussed by M. Marcus and B. N. Moyls in the paper ''Linear Transformations on Algebras of Matrices". The authors were able to characterize linear transformations which preserve one or more of the following properties of n-square matrices; rank, determinant and eigenvalues. The problem of obtaining a similar characterization of transformations as given by M. Marcus and B. N. Moyls but for a wider class of fields is considered in this thesis. In particular, their characterization of rank preserving transformations holds for an arbitrary field. One of the results on determinant preserving transformations obtained by M. Marcus and B. N. Moyls states that if a linear transformation T maps unimodular matrices into unimodular matrices, then T preserves determinants. Since this result does not necessarily hold for algebras of matrices over finite fields, the discussion on the characterization of determinant preserving transformations is limited to algebras of matrices over infinite fields. / Science, Faculty of / Mathematics, Department of / Graduate

We consider naturally occurring, uncountable transformation semigroups S and investigate the following three questions. (i) Is every countable subset F of S also a subset of a finitely generated subsemigroup of S? If so, what is the least number n such that for every countable subset F of S there exist n elements of S that generate a subsemigroup of S containing F as a subset. (ii) Given a subset U of S, what is the least cardinality of a subset A of S such that the union of A and U is a generating set for S? (iii) Define a preorder relation ≤ on the subsets of S as follows. For subsets V and W of S write V ≤ W if there exists a countable subset C of S such that V is contained in the semigroup generated by the union of W and C. Given a subset U of S, where does U lie in the preorder ≤ on subsets of S? Semigroups S for which we answer question (i) include: the semigroups of the injec- tive functions and the surjective functions on a countably infinite set; the semigroups of the increasing functions, the Lebesgue measurable functions, and the differentiable functions on the closed unit interval [0, 1]; and the endomorphism semigroup of the random graph. We investigate questions (ii) and (iii) in the case where S is the semigroup Ω[superscript Ω] of all functions on a countably infinite set Ω. Subsets U of Ω[superscript Ω] under consideration are semigroups of Lipschitz functions on Ω with respect to discrete metrics on Ω and semigroups of endomorphisms of binary relations on Ω such as graphs or preorders.