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

Ce travail s'inscrit dans le cadre d'un partenariat scientifique entre le Laboratoire Navier et la société STRAINS. Convaincue du besoin de renouveler les méthodes actuelles de calcul de structures, STRAINS développe un nouveau logiciel dédié à l'analyse des ouvrages d'art. Dans ce contexte, cette thèse propose de nouveaux outils pour l'analyse des structures élancées. Le modèle élastique de poutre d'ordre supérieur développé par cite{Ferradi2016} est d'abord adapté au cas des déformations imposées, permettant ainsi au modèle de représenter un grand nombre de phénomènes physiques tels que le fluage, la précontrainte ou les chargements thermiques. Différents exemples viennent souligner la précision numérique du modèle ainsi que ses performances en temps de calcul. Le modèle est également étendu au cadre de la théorie de la plasticité. Considérant les déformations plastiques comme des déformations imposées, les résultats précédemment obtenus sont utilisés pour développer une nouvelle cinématique d'ordre supérieur. Enfin, un nouvel élément de poutre élastoplastique pour le béton armé est proposé. Le béton est décrit grâce au modèle élastoplastique et les ferraillages sont modélisés par des éléments barres à une dimension. Cette méthode permet une description précise du comportement du béton et une représentation fidèle des renforcements. La validité des calculs est évaluée par des considérations de dissipation énergétique / This thesis work is presented in the framework of a scientific partnership between Laboratoire Navier and the french start-up STRAINS. Believing in the need for new methodologies in structural analysis, STRAINS is developing a new software dedicated to the structural analysis of bridges. In this context, this work suggests new tools for the analysis of slender structures.The higher-order elastic beam element developed by cite{Ferradi2016} is first extended to the case of eigenstrains, enabling the model to deal with various physical phenomena such as creep, prestress or thermal loads. An enriched kinematics is used to capture the local response of the structure. Different examples highlight the local accuracy of the model and its fast computational performances. The model is also extended to plasticity in small perturbations. Considering the plastic strains developing in the structure as eigenstrains, the previous works are used to derive a higher-order elastoplastic kinematics.Finally, a new elastoplastic beam element for reinforced concrete is suggested. The concrete material is described by using the elastoplastic beam model developed previously while steel rebars are modeled by one dimensional bar elements. This method enables a fine local description of the concrete behavior and an accurate representation of the reinforcement. The validity of computations is assessed thanks to energy considerations

The double-mean-reverting model by Gatheral is motivated by empirical dynamics of the variance of the stock price. No closed-form solution for European option exists in the above model. We study the behaviour of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at-the-money. Using the method by Pagliarani and Pascucci, we calculate explicitly the first few terms of the asymptotic expansion of the implied volatility within a parabolic region.

In this thesis, two topics in asymptotic statistics and spline functions are studied. / The first one is a study of testing the equality of Sharpe ratios. We compare two approaches to testing for the equality of many Sharpe ratios: the multivariate test of Wright et al. (2014) and Ledoit and Wolf's (2008) pairwise test. Firstly, Ledoit and Wolf's pairwise test is generalized to a multivariate one for direct comparison. We conclude by proposing a modified version that incorporates the Warp-Speed calibration method of Giacomini et al. (2013). The resulting procedure is much less computationally expensive but is comparable in its accuracy. / The second one is a study of the theoretical properties of an exponential weighting aggregated (EWA) penalized spline estimator, where the smoothing parameter is being averaged over an exponential reweighted posterior distribution. We show that the finite sample mean squared error of the EWA estimator is smaller than that of the smooth penalized spline estimator when the smoothing parameter is chosen to be a fixed value. Consistency and asymptotic normality of the EWA estimator are also developed under general situations. / 這篇論文研究了兩個關於漸近統計和樣條函數的話題。 / 其一是在假設檢驗夏普比率的相等性這個問題中的應用。我們首先比較了Wright et al.（2014）的多元檢驗方法和Ledoit & Wolf（2008）的二元檢驗方法。我們先將Ledoit & Wolf (2008)的二元檢驗法拓展到多元層面，以方便比較。最後，我們提出了採用Giacomini et al.（2013）的曲速法修改后的自助抽樣檢驗法。這種方法極大地降低了實際計算成本，同時保持了其準確性。 / 其二是對樣條估計的漸近表現的研究。我們研究了指數權重合計平滑樣條（EWA）估計，這種方法通過貝葉斯法給予平滑參數一個後驗分佈并將其加權合計。我們通過擴展一個oracle不等式驗證了EWA估計的方差比選定了一個平滑參數的一般平滑樣條估計的方差要小。此外，我們還驗證了EWA估計在一般情況下的一致性和漸近正態性。 / Huang, Wei. / Thesis M.Phil. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 80-84). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

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

by Choi Chun-Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 56-58). / Abstract also in Chinese. / Chapter 1 --- Radial symmetry for solutions of a semilinear el- liptic equation on a bounded domain --- p.6 / Chapter 2 --- Asymptotic symmetry of singular solutions to a semilinear elliptic equation --- p.12 / Chapter 2.1 --- Introduction --- p.12 / Chapter 2.2 --- Some preliminary analysis --- p.14 / Chapter 2.3 --- Proof of Theorem 2.1 --- p.20 / Chapter 3 --- Classification of non-negative solutions to Yamabe type equations --- p.32 / Chapter 3.1 --- Introduction --- p.32 / Chapter 3.2 --- The Proof of Theorem 3.1 for k > 0 --- p.38 / Chapter 3.3 --- Case k <0 --- p.48 / Bibliography

A partir de uma aplicação da Forma Canônica de Jordan, construímos uma base para o espaço atrator para operadores quânticos de dimensão finita. Essa base é formada pelos autoespaços correspondentes a autovalores de módulo 1. Com essa construção, descrevemos o comportamento da dinâmica assint otica dos operadores quânticos, obtendo assim, o resultado principal do texto. A dinâmica depende dos vetores duais, cuja definição não é feita a partir de uma forma explicita, mas por propriedades relacionadas ao traço. Investigando propriedades dos operadores estritamente positivos, definimos um produto interno que relaciona o produto interno de Hilbert-Schmidt com um operador estritamente positivo. Com isso, obtemos uma forma explícita para os vetores duais. / From an application of the Jordan Canonical Form, we construct a basis for the attractor space for quantum operations of nite dimension. This basis is formed by eigenspaces corresponding to eigenvalues of modulus 1. With this construction, we describe the behavior of the asymptotic dynamics of the quantum operations, thus obtaining the main result of the text. The dynamics depends on the dual vectors whose de nition is not made in an explicit form, but by properties related to the trace. Investigating the properties of strictly positive operators, we de ne an inner product that relates the Hilbert-Schmidt inner product with a strictly positive operator. Thus, we have an explicit form for the dual vectors.

Geng Di. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 116-119). / Acknowledgement --- p.i / Abstract --- p.ii / Introduction --- p.iii / Part I --- p.1 / Chapter 1 --- Critical Dimension of a Semilinear Degenerate Elliptic Equation Involving Critical Sobolev-Hardy Exponent --- p.2 / Chapter 1.1 --- Introduction --- p.2 / Chapter 1.2 --- Non-existence (I) --- p.5 / Chapter 1.3 --- Non-existence (II) --- p.11 / Chapter 1.4 --- Existence --- p.13 / Chapter 1.5 --- Radial Symmetry of Solutions --- p.16 / Appendix A --- p.20 / Appendix B --- p.23 / Chapter 2 --- Critical Dimension of a Hessian Equation Involving Critical Ex- ponent --- p.27 / Chapter 2.1 --- Introduction --- p.27 / Chapter 2.2 --- Preliminary Results --- p.29 / Chapter 2.3 --- Existence Results --- p.32 / Chapter 2.4 --- Non-existence Results --- p.43 / Chapter 3 --- Absence of Critical Dimension for the Subelliptic Laplacian on the Heisenberg Group --- p.48 / Chapter 3.1 --- Introduction and Main Result --- p.48 / Chapter 3.2 --- Proof of the Theorem --- p.49 / Part2 --- p.55 / Chapter 4 --- Asymptotic Behavior for Weighted p-Laplace Equations Involv- ing Critical Growth on the Ball --- p.56 / Chapter 4.1 --- Introduction --- p.56 / Chapter 4.2 --- A Crucial Lemma --- p.59 / Chapter 4.3 --- Proof of the Main Theorems --- p.61 / Chapter 5 --- Asymptotics for a Semilinear Weighted Elliptic Equation In- volving Critical Sobolev-Hardy Exponent --- p.71 / Chapter 5.1 --- Introduction --- p.71 / Chapter 5.2 --- Some Preliminary Results --- p.73 / Chapter 5.3 --- A Crucial Estimate --- p.80 / Chapter 5.4 --- Proof of the Main Theorem --- p.85 / Appendix --- p.88 / Chapter 6 --- Asymptotics for Positive Solutions for a Biharmonic Equation Involving Critical Exponent --- p.93 / Chapter 6.1 --- Introduction --- p.93 / Chapter 6.2 --- Preliminary Results --- p.94 / Chapter 6.3 --- Pohozaev's identity and Green's Function --- p.98 / Chapter 6.4 --- A Crucial Lemma --- p.103 / Chapter 6.5 --- Proof of Main Theorem --- p.112 / Bibliography --- p.115

Observational studies are an indispensable complement to randomized clinical trials (RCT) for comparison of treatment effectiveness. Often RCTs cannot be carried out due to the costs of the trial, ethical questions and rarity of the outcome. When noncompliance and missing data are prevalent, RCTs become more like observational studies. The main problem is to adjust for the selection bias in the observational study. One increasingly used method is propensity-score matching. Compared to traditional multi-covariate matching methods, matching on the propensity score alleviates the curse of dimensionality. It allows investigators to balance multiple covariate distributions between treatment groups by matching on a single score. This thesis focuses on the large sample properties of the matching estimators of the treatment effect. The first part of this thesis deals with problems of the analytic supports of the logit propensity score and various matching methods. The second part of this thesis focuses on the matching estimators of additive and multiplicative treatment effects. We derive the asymptotic order of the biases and asymptotic distributions of the matching estimators. We also derive the large sample variance estimators for the treatment effect estimators. The methods and theoretical results are applied and checked in a series of simulation studies. The third part of this thesis is devoted to a comparison between propensity-score matching and multiple linear regression using simulation.