La recherche sur les méthodes bayésiennes non-paramétriques connaît un essor considérable depuis les vingt dernières années notamment depuis le développement d'algorithmes de simulation permettant leur mise en pratique. Il est donc nécessaire de comprendre, d'un point de vue théorique, le comportement de ces méthodes. Cette thèse présente différentes contributions à l'analyse des propriétés fréquentistes des méthodes bayésiennes non-paramétriques. Si se placer dans un cadre asymptotique peut paraître restrictif de prime abord, cela permet néanmoins d'appréhender le fonctionnement des procédures bayésiennes dans des modèles extrêmement complexes. Cela permet notamment de détecter les aspects de l'a priori particulièrement influents sur l’inférence. De nombreux résultats généraux ont été obtenus dans ce cadre, cependant au fur et à mesure que les modèles deviennent de plus en plus complexes, de plus en plus réalistes, ces derniers s'écartent des hypothèses classiques et ne sont plus couverts par la théorie existante. Outre l'intérêt intrinsèque de l'étude d'un modèle spécifique ne satisfaisant pas les hypothèses classiques, cela permet aussi de mieux comprendre les mécanismes qui gouvernent le fonctionnement des méthodes bayésiennes non-paramétriques. / Research on Bayesian nonparametric methods has received a growing interest for the past twenty years, especially since the development of powerful simulation algorithms which makes the implementation of complex Bayesian methods possible. From that point it is necessary to understand from a theoretical point of view the behaviour of Bayesian nonparametric methods. This thesis presents various contributions to the study of frequentist properties of Bayesian nonparametric procedures. Although studying these methods from an asymptotic angle may seems restrictive, it allows to grasp the operation of the Bayesian machinery in extremely complex models. Furthermore, this approach is particularly useful to detect the characteristics of the prior that are strongly influential in the inference. Many general results have been proposed in the literature in this setting, however the more complex and realistic the models the further they get from the usual assumptions. Thus many models that are of great interest in practice are not covered by the general theory. If the study of a model that does not fall under the general theory has an interest on its owns, it also allows for a better understanding of the behaviour of Bayesian nonparametric methods in a general setting.

Les roues aubagées de turbomachines sont soumises en fonctionnement `a des sollicitations statiqueset dynamiques, qui peuvent conduire `a des situations de fatigue vibratoire pour des excitationsau voisinage des fréquences de résonance. Ce probléme est aggravé par le désaccordage involontaire,auquel sont sujets les ensembles aubagés notamment du fait des dispersions de fabrication.L’objectif de ce travail de recherche est de proposer une stratégie mixte numérique et expérimentalepermettant de caractériser le comportement dynamique d’une roue d’essai au sein des statistiquesdécrivant une flotte simulée de moteurs en service, en vue de la certification vibratoire. Un modèle numérique fidèle basée sur l’acquisition optique d’une roue expérimentale a été développé; une série d’essais en laboratoire a permis de vérifier sa représentativité. L’exploitation de mesures réalisées en configuration moteur a montré une bonne cohérence globale des niveaux d’amplitude prédits à l’aidedu modèle fidèle. Enfin, la simulation du comportement d’une population de roues désaccordées à l’aide d’une approche probabiliste non-Paramétrique a permis de positionner l’amplitude de réponse maximale rencontrée sur la pièce d’essai par rapport à la valeur théorique obtenue par simulation. La stratégie proposée permet une prédiction des niveaux vibratoires maximaux pour une flotte de rouesen service. / Under operating conditions, turbomachinery blisks are subject to static and dynamic loads which mayresult in High-Cycle Fatigue situations when excited at the neighbourhood of resonant frequencies.Random mistuning, which affects blisks due to machining deviations, turns this issue even morecritical. The objective of the current study is to introduce a numerical-Experimental strategy allowingthe dynamic characterization of an experimental bladed disk with regard to the statistics representingthe simulated behaviour for a population of operating blisks. A high-Fidelity numerical model basedon the optical acquisition of an experimental blisk has been set up. Test series performed in labconditions allowed to verify its coherence. The comparison of the response amplitudes measuredunder operating conditions to the model predictions revealed an acceptable matching between testand simulation data. Finally, a non-Parametric probabilistic approach has been used to predict thetheoretical maximal amplification factor. The maximum amplification factor obtained by means ofsimulation was compared to the amplification factor of the test specimen. The strategy proposed inthis study allows maximum amplification factor predictions for a population of blisks

Préfigurant la prochaine grande étape dans le domaine de la navigation, la géolocalisation intra-muros est un domaine de recherche très actif depuis quelques années. Alors que la géolocalisation est entrée dans le quotidien de nombreux professionnels et particuliers avec, notamment, le guidage routier assisté, les besoins d'étendre les applications à l'intérieur se font de plus en plus pressants. Cependant, les systèmes existants se heurtent à des contraintes techniques bien supérieures à celles rencontrées à l'extérieur, la faute, notamment, à la propagation chaotique des ondes électromagnétiques dans les environnements confinés et inhomogènes. Nous proposons dans ce manuscrit une approche statistique du problème de géolocalisation d'un mobile à l'intérieur d'un bâtiment utilisant les ondes WiFi environnantes. Ce manuscrit s'articule autour de deux questions centrales : celle de la détermination des cartes de propagation des ondes WiFi dans un bâtiment donné et celle de la construction d'estimateurs des positions du mobile à l'aide de ces cartes de propagation. Le cadre statistique utilisé dans cette thèse afin de répondre à ces questions est celui des modèles de Markov cachés. Nous proposons notamment, dans un cadre paramétrique, une méthode d'inférence permettant l'estimation en ligne des cartes de propagation, sur la base des informations relevées par le mobile. Dans un cadre non-paramétrique, nous avons étudié la possibilité d'estimer les cartes de propagation considérées comme simple fonction régulière sur l'environnement à géolocaliser. Nos résultats sur l'estimation non paramétrique dans les modèles de Markov cachés permettent d'exhiber un estimateur des fonctions de propagation dont la consistance est établie dans un cadre général. La dernière partie du manuscrit porte sur l'estimation de l'arbre de contextes dans les modèles de Markov cachés à longueur variable. / Foreshadowing the next big step in the field of navigation, indoor geolocation has been a very active field of research in the last few years. While geolocation entered the life of many individuals and professionals, particularly through assisted navigation systems on roads, needs to extend the applications inside the buildings are more and more present. However, existing systems face many more technical constraints than those encountered outside, including the chaotic propagation of electromagnetic waves in confined and inhomogeneous environments. In this manuscript, we propose a statistical approach to the problem of geolocation of a mobile device inside a building, using the WiFi surrounding waves. This manuscript focuses on two central issues: the determination of WiFi wave propagation maps inside a building and the construction of estimators of the mobile's positions using these propagation maps. The statistical framework used in this thesis to answer these questions is that of hidden Markov models. We propose, in a parametric framework, an inference method for the online estimation of the propagation maps, on the basis of the informations reported by the mobile. In a nonparametric framework, we investigated the possibility of estimating the propagation maps considered as a single regular function on the environment that we wish to geolocate. Our results on the nonparametric estimation in hidden Markov models make it possible to produce estimators of the propagation functions whose consistency is established in a general framework. The last part of the manuscript deals with the estimation of the context tree in variable length hidden Markov models.

L'objectif de ce travail est de développer de nouvelles méthodes statistiques de reconstruction d'image spatiale (3D) et spatio-temporelle (3D+t) en Tomographie par Émission de Positons (TEP). Le but est de proposer des méthodes efficaces, capables de reconstruire des images dans un contexte de faibles doses injectées tout en préservant la qualité de l'interprétation. Ainsi, nous avons abordé la reconstruction sous la forme d'un problème inverse spatial et spatio-temporel (à observations ponctuelles) dans un cadre bayésien non paramétrique. La modélisation bayésienne fournit un cadre pour la régularisation du problème inverse mal posé au travers de l'introduction d'une information dite a priori. De plus, elle caractérise les grandeurs à estimer par leur distribution a posteriori, ce qui rend accessible la distribution de l'incertitude associée à la reconstruction. L'approche non paramétrique quant à elle pourvoit la modélisation d'une grande robustesse et d'une grande flexibilité. Notre méthodologie consiste à considérer l'image comme une densité de probabilité dans (pour une reconstruction en k dimensions) et à chercher la solution parmi l'ensemble des densités de probabilité de . La grande dimensionalité des données à manipuler conduit à des estimateurs n'ayant pas de forme explicite. Cela implique l'utilisation de techniques d'approximation pour l'inférence. La plupart de ces techniques sont basées sur les méthodes de Monte-Carlo par chaînes de Markov (MCMC). Dans l'approche bayésienne non paramétrique, nous sommes confrontés à la difficulté majeure de générer aléatoirement des objets de dimension infinie sur un calculateur. Nous avons donc développé une nouvelle méthode d'échantillonnage qui allie à la fois bonnes capacités de mélange et possibilité d'être parallélisé afin de traiter de gros volumes de données. L'approche adoptée nous a permis d'obtenir des reconstructions spatiales 3D sans nécessiter de voxellisation de l'espace, et des reconstructions spatio-temporelles 4D sans discrétisation en amont ni dans l'espace ni dans le temps. De plus, on peut quantifier l'erreur associée à l'estimation statistique au travers des intervalles de crédibilité. / The aim of this work is to develop new statistical methods for spatial (3D) and space-time (3D+t) Positron Emission Tomography (PET) reconstruction. The objective is to propose efficient reconstruction methods in a context of low injected doses while maintaining the quality of the interpretation. We tackle the reconstruction problem as a spatial or a space-time inverse problem for point observations in a \Bayesian nonparametric framework. The Bayesian modeling allows to regularize the ill-posed inverse problem via the introduction of a prior information. Furthermore, by characterizing the unknowns with their posterior distributions, the Bayesian context allows to handle the uncertainty associated to the reconstruction process. Being nonparametric offers a framework for robustness and flexibility to perform the modeling. In the proposed methodology, we view the image to reconstruct as a probability density in(for reconstruction in k dimensions) and seek the solution in the space of whole probability densities in . However, due to the size of the data, posterior estimators are intractable and approximation techniques are needed for posterior inference. Most of these techniques are based on Markov Chain Monte-Carlo methods (MCMC). In the Bayesian nonparametric approach, a major difficulty raises in randomly sampling infinite dimensional objects in a computer. We have developed a new sampling method which combines both good mixing properties and the possibility to be implemented on a parallel computer in order to deal with large data sets. Thanks to the taken approach, we obtain 3D spatial reconstructions without any ad hoc space voxellization and 4D space-time reconstructions without any discretization, neither in space nor in time. Furthermore, one can quantify the error associated to the statistical estimation using the credibility intervals.

La théorie des graphes a longtemps été étudiée en mathématiques et en probabilité en tant qu’outil pour décrire la dépendance entre les nœuds. Cependant, ce n’est que récemment qu’elle a été mise en œuvre sur des données, donnant naissance à l’analyse statistique des réseaux réels.La topologie des réseaux économiques et financiers est remarquablement complexe: elle n’est généralement pas observée, et elle nécessite ainsi des procédures inférentielles adéquates pour son estimation, d’ailleurs non seulement les nœuds, mais la structure de la dépendance elle-même évolue dans le temps. Des outils statistiques et économétriques pour modéliser la dynamique de changement de la structure du réseau font défaut, malgré leurs besoins croissants dans plusieurs domaines de recherche. En même temps, avec le début de l’ère des “Big data”, la taille des ensembles de données disponibles devient de plus en plus élevée et leur structure interne devient de plus en plus complexe, entravant les processus inférentiels traditionnels dans plusieurs cas. Cette thèse a pour but de contribuer à ce nouveau champ littéraire qui associe probabilités, économie, physique et sociologie en proposant de nouvelles méthodologies statistiques et économétriques pour l’étude de l’évolution temporelle des structures en réseau de moyenne et haute dimension. / Graph theory has long been studied in mathematics and probability as a tool for describing dependence between nodes. However, only recently it has been implemented on data, giving birth to the statistical analysis of real networks.The topology of economic and financial networks is remarkably complex: it is generally unobserved, thus requiring adequate inferential procedures for it estimation, moreover not only the nodes, but the structure of dependence itself evolves over time. Statistical and econometric tools for modelling the dynamics of change of the network structure are lacking, despite their increasing requirement in several fields of research. At the same time, with the beginning of the era of “Big data” the size of available datasets is becoming increasingly high and their internal structure is growing in complexity, hampering traditional inferential processes in multiple cases.This thesis aims at contributing to this newborn field of literature which joins probability, economics, physics and sociology by proposing novel statistical and econometric methodologies for the study of the temporal evolution of network structures of medium-high dimension.

Nesta dissertação apresentamos métodos de diagnóstico em modelos semiparamétricos sob erros normais, em especial os modelos semiparamétricos com uma variável explicativa não paramétrica, conhecidos como modelos lineares parciais. São utilizados splines cúbicos para o ajuste da variável resposta e são aplicadas funções de verossimilhança penalizadas para a obtenção dos estimadores de máxima verossimilhança com os respectivos erros padrão aproximados. São derivadas também as propriedades da matriz hat para esse tipo de modelo, com o objetivo de utilizá-la como ferramenta na análise de diagnóstico. Gráficos normais de probabilidade com envelope gerado também foram adaptados para avaliar a adequabilidade do modelo. Finalmente, são apresentados dois exemplos ilustrativos em que os ajustes são comparados com modelos lineares normais usuais, tanto no contexto do modelo aditivo normal simples como no contexto do modelo linear parcial. / In this master dissertation we present diagnostic methods in semiparametric models under normal errors, specially in semiparametric models with one nonparametric explanatory variable, also known as partial linear model. We use cubic splines for the nonparametric fitting, and penalized likelihood functions are applied for obtaining maximum likelihood estimators with their respective approximate standard errors. The properties of the hat matrix are also derived for this kind of model, aiming to use it as a tool for diagnostic analysis. Normal probability plots with simulated envelope graphs were also adapted to evaluate the model suitability. Finally, two illustrative examples are presented, in which the fits are compared with usual normal linear models, such as simple normal additive and partially linear models.

A neuropatia diabética causa diminuição ou perda da sensibilidade protetora do pé, tornando-o mais vulnerável ao trauma mecânico e térmico. A profilaxia das complicações neuropáticas tem início pela identificação da perda de sensibilidade e, portanto, do comprometimento neurológico. O Pressure Specified Sensory Device(TM) (PSSD) é um equipamento desenvolvido para quantificar o limiar de pressão, aplicada sobre a pele, necessária para que o paciente perceba o estímulo provocado por: um ponto estático, um ponto em movimento, dois pontos estáticos e dois pontos em movimento. Denominamos grupo estudo, aos trinta e quatro pacientes diabéticos do tipo 2, sem história prévia de feridas e/ou amputações nos pés que foram submetidos à avaliação de sensibilidade cutânea utilizando-se o PSSD(TM). Foram realizados testes nos territórios cutâneos dos nervos fibular profundo, plantar medial e ramo calcâneo do nervo tibial posterior. Estímulos foram provocados segundo as modalidades: um ponto estático (1 PE), um ponto em movimento (1 PD), dois pontos estáticos (2 PE) e dois pontos em movimento (2 PD), para as duas últimas modalidades. Previamente às modalidades 2PE e 2PD determinou-se o limiar de discriminação entre dois pontos estáticos (D2PE) e em movimento (D2PD). Foram realizados apenas no grupo estudo, testes com o monofilamento de Semmes-Weisntein nº 5,07 (MSW) e com o diapasão de 128 Hz. Vinte e oito pacientes não-diabéticos, submetidos aos mesmos testes, formaram o grupo controle. Para os limiares de sensibilidade, encontramos valores superiores no grupo estudo (p < 0,05). Ao compararmos os limiares de sensibilidade alcançados pelos pacientes diabéticos sensíveis e não sensíveis ao estímulo promovido pelo MSW nº 5,07 verificamos que o p-valor variou entre 0,018 < p < 0,113 para 1 PE e 0,002 < p < 0,083 para 2 PE, conforme o território cutâneo estudado. Na comparação dos limiares de sensibilidade da modalidade 1 PD entre diabéticos sensíveis e insensíveis à vibração do diapasão de 128 Hz, as diferenças não foram estatisticamente significantes (p = 0,183). Os resultados obtidos nos permitiram sugerir que o dispositivo PSSD(TM) seja utilizado como forma de acompanhamento do comprometimento da fibra nervosa. / Neuropathy is a severe progressive loss of protective sensation on the feet, making the patient more vulnerable to mechanical trauma and consequently more suitable to the development of chronic wounds, major distortion of the foot bone architecture and eventually to limb amputation. Prophylaxis should be enforced to avoid foot ulceration and for that, evaluation of the degree of loss of sensation on the skin is essential. The PSSD (Pressure Specified Sensory Device(TM)) was developed in order to quantify the threshold of pressure applied to the skin that could be recognized as positive by the patient. Pressure of one or two points is tested both statically and with movement, thus assessing the function of fast and slow response nerve fibers. Threshold of two-point discrimination was also measured in mm. Thirty four (n = 34) diabetic patients, type II, with no previous history of wounds on the lower extremity were studied using the tests, one point static (1PE), one point moving (1PD) and two points static (2 PE), and moving (2 PD) on the cutaneous territory of the fibular nerve and posterior tibial nerve (two territories - medial plantar and calcaneous nerves). The control group (28 non diabetic patients) was assessed by the same exams and the results were compared. In the diabetic group the cutaneous territories were also evaluated using the conventional Semmes-Weinstein filament nº 5,07 e vibrometer of the 128 Hz. Altered values were observed for the static and dynamic tests over the three studied nerve territories. The differences were statically significant (p < 0,05). Comparing the threshold of sensibility between sensitive and non sensitive diabetic patients to MSW nº 5,07 test, we observed that p-value range was 0,018 0,113 when 1PE test was applied, and 0,002 0,083 when 2PE test was applied, according to the cutaneous territories evaluated. Numeric quantification of the threshold of pressure allows us to determine the status of the fiber/receptor structures as well as the functional deficit of nerve fibers. Our findings suggest that PSSD(TM) is an adjuvant tool to evaluate the degree of loss of sensation on the skin.

A pesquisa procurou levantar a relação entre concentração acionária e risco de expropriação de riqueza dos credores no Brasil. O universo amostral compreendeu as empresas de capital aberto listadas na Bovespa no período de 1997 a 2011. Foram traçados dois objetivos na pesquisa: (i) verificar se empresas com a presença de controle acionário definido apresentam maior percepção de risco de expropriação de riqueza dos credores do que aquelas que não apresentam concentração acionária; e (ii) verificar entre as empresas com a presença de controle acionário definido se maior participação no controle gera maior percepção de risco de expropriação de riqueza de terceiros. O suporte teórico do trabalho se deu em estudos sobre estrutura de capital, controle de capital, mercado de crédito e custo de capital de terceiros no Brasil. As variáveis estudadas foram o percentual de ações ON pelos principais acionistas e o custo da dívida medido pelo Ki. Os procedimentos estatísticos se deram pelos testes não paramétricos U de Man-Whitney e Kruskal-Wallis com comparações múltiplas entre grupos. A primeira resposta apresentou indícios, com significância estatística de 5%, que empresas com controle acionário definido tendem a apresentar maior risco de expropriação de riqueza de terceiros do que as demais. Entretanto, quando o controle é exercido por um único acionista que possui 50% ou mais das ações com direito a voto, as empresas tendem a apresentar menor risco de expropriação de riqueza dos credores do que as demais. A segunda resposta encontrada, também com significância estatística de 5%, apontou que, em empresas com a presença de um único acionista na posse de 50% ou mais das ações ON, à medida que esse principal acionista aumenta a participação no controle, o custo da dívida, variável explicativa de risco de expropriação de riqueza de terceiros, tende a diminuir. Portanto, acredita-se que o presente estudo cumpre a proposta de investigação apresentada ao não encontrar evidências que permitam descartar a ideia de que existe relação entre controle acionário definido e risco de expropriação de riqueza dos credores.Palavras-chave: Apreçamento de opções, Modelo HJM Gaussiano, Regressão não paramétrica. / The survey tried to raise the relationship between ownership concentration and risk of expropriation of creditors\' wealth in Brazil. The sample universe consisted of publicly traded companies listed on Bovespa in the period 1997-2011. Two main objectives were outlined: (i) verify if companies with the presence of defined shareholder control have a higher perception of risk of expropriation of creditors\' wealth than those who do not have shareholder control, and (ii) check between companies with defined shareholder control set if greater participation in the control creates higher perception of risk of expropriation of third parties\' wealth. The theoretical basis of the work was in studies on capital structure, capital controls, credit market and cost of third party capital in Brazil. The variables studied were the percentage of ON shares by principal shareholders and the cost of debt measured by Ki. Statistical procedures were given by nonparametric tests U of Mann Whitney and Kruskal-Wallis with multiple comparisons between groups. The first response, with statistical significance of 5%, showed that companies with defined shareholder control set tend to have a higher risk of expropriation of third parties\' wealth than others. However, when the control is exercised by a single shareholder who holds 50% or more of voting shares, companies tend to have lower risk of expropriation of creditors\' wealth than others. The second one, also with a statistical significance of 5%, pointed out that in companies with a single shareholder who holds 50% or more of ON shares, as this principal shareholder increases his participation in the control, the cost of debt, explanatory variable risk of expropriation of third parties\' wealth, tends to decrease. Therefore, it is believed that this study fulfils the investigation proposal presented to find no evidence to discard the idea that there is a relationship between defined shareholder control and risk of expropriation of creditors\' wealth.

A análise de regressão kernel não paramétrica desconsidera qualquer influência das formas funcionais geralmente empregadas em análises de regressões paramétricas, permitindo os dados \"falarem por si mesmos\". Enquanto os estimadores paramétricos são considerados globais, os kernels não paramétricos usam uma amostra de dados próximas (definida pela largura da janela) a um ponto para ajustar a estimação, o que permite focar em peculiaridades locais dos dados. Ambas as análises foram aplicadas aos dados do Censo Agropecuário de 2006 realizado pelo IBGE, agregados municipalmente e em dezessete faixas de áreas, para estimar uma função de produção com o objetivo de estabelecer a relação entre o tamanho das propriedades agrícolas e o valor da produção por hectare (produtividade). A relação constatada foi inversa, porém a análise local feita pelos estimadores kernels explicitou uma relação direta entre as elasticidades de produção dos insumos e o tamanho das propriedades agrícolas, o que não justifica uma política de redistribuição de terras no sentido do aumento da produtividade. Além disto, análises gráficas contra fatuais (que manteve os insumos, exceto a área, constantes em seus valores médios) mostraram que a relação não é linear, não é monotônica, e difere dentre as regiões, o que é um desafio para a elaboração de políticas de redistribuição de terras. / Nonparametric kernel regression analysis disregards any influence of the functional forms commonly employed in parametric regression analyzes, allowing the data to \"speak for itself.\" While parametric estimators are considered global, nonparametric kernels use a sample of nearby data (defined by the bandwidth) at a point to adjust the estimation, which allows focusing on local peculiarities of the data. Both analyzes were applied to data from the 2006 IBGE Census of Agriculture, aggregated in municipalities and in seventeen areas, to estimate a production function with the objective of establishing the relationship between the size of agricultural properties and the value of production by hectare (productivity). The observed relationship was reversed, but the local analysis made by the kernels estimators explained a direct relationship between the elasticities of production of the inputs and the size of the agricultural properties, which does not justify a policy of redistribution of land in order to increase productivity. In addition, graphical analyzes against factors (which kept the inputs, except the area, constant in their mean values) showed that the relationship is not linear, is not monotonic, and differs among regions, which is a challenge for the elaboration of land redistribution policies.

O objetivo principal deste trabalho é discutir estimação e diagnóstico em modelos semiparamétricos com resposta binomial negativa, mais especificamente, modelos de regressão com resposta binomial negativa em que uma das variáveis explicativas contínuas é modelada de forma não paramétrica. Iniciamos o trabalho com um exemplo ilustrativo e fazemos uma breve revisão dos modelos paramétricos com resposta binomial negativa. Em seguida, introduzimos os modelos semiparamétricos com resposta binomial negativa e discutimos alguns aspectos de estimação, inferência e seleção de modelos. Dedicamos um capítulo a procedimentos de diagnóstico, tais como desenvolvimento de medidas de alavanca e de influência sob os aspectos de deleção de pontos e influência local, além de abordar a análise de resíduos. Reanalizamos o exemplo ilustrativo sob o enfoque semiparamétrico e apresentamos algumas conclusões. / The aim of this work is to discuss some aspects on estimation and diagnostics in negative binomial regression models which an explanatory continuous variable is modeled nonparametrically. First, an illustrative example is presented and analyzed under parametric negative binomial regression models. The proposed models are then introduced and some aspects on estimations, inference and model selection are presented. Particular emphasis is given on the development of diagnostic procedures, such as leverage measures, Cook distances, local influence approach and residuals. The motivated example is reanalyzed under the semiparametric viewpoint and some conclusions are given.