This thesis deals with a finding ideal transformation which can model data well. We focus on transformations which we know up to a parametr. We need to estimate the parametr of the transformation. The main approach of study transformation is in linear regression and in nonparametric regression. In both cases we focus on estimating the transformation parametr and properties of this estimator such as consistency and asymptotic normality. We show in linear regression that the aprroach of least squares do not work properly. Instead of this we use a generalized moment method which can estimate parametr of transformation and also a regression coefficients. We show also a different solution for our problem in specific transformation called Box-Cox. For this situation we make a simulation study for estimators and standard deviations. The standard deviation are obtained by bootstrap method. In nonparametric regression we use profile likelihood to estimate transformation parametr. We also construct an estimator of density of error terms. In both cases we know the asymptotic distribution.

In this thesis, we study the estimation of the nonlinear conditionalrisk-neutral density function (RND) in discrete time. Specifically, weevaluate the extent to which the estimated nonlinear conditional RNDvaluable insights to answer relevant economic questions regarding to optionpricing, the measurement of invertors' preferences and portfolio choice.We make use of large dataset of options contracts written on the S&P 500index from 1996 to 2011, to estimate the parameters of the conditional RNDfunctions by minimizing the squared option pricing errors delivered by thenonlinear models studied in the thesis.In the first essay, we show that a semi-nonparametric option pricing modelwith GARCH variance outperforms several benchmarks models in-sample andout-of-sample. In the second essay, we show that a simple two-state regimeswitching model in volatility is not able to fully account for the pricingkernel and the risk aversion puzzle; however, it provides a reasonablecharacterisation of the time-series properties of the estimated riskaversion.In the third essay, we evaluate linear stochastic discount factormodels using an out-of-sample financial metric. We find that multifactormodels outperform the CAPM when this metric is used, and that modelsproducing the best fit in-sample are also those exhibiting the bestperformance out-of-sample.

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.

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.

Cette thèse cherche à approfondir la nature et la forme des relations entre les inégalités éducatives et le développement. Elle s’inscrit dans le prolongement des analyses engagées sur les liens éducation/croissance et inégalités/croissance, en essayant d’apporter un éclairage complémentaire sur ces deux relations. Elle vise à retracer de manière stylisée l’évolution des inégalités éducatives particulièrement dans les pays en développement et à caractériser la non-linéarité de la relation à partir de l’estimation de modèles non-paramétriques et semi-paramétriques. Cette thèse est constituée de trois chapitres auxquels correspondent des objectifs, des bases de données et des méthodologies spécifiques. Dans un premier chapitre, nous proposons une nouvelle base mondiale sur les inégalités d’éducation. La majorité des travaux sur la relation entre capital humain et développement économique ont principalement appréhendé la mesure du capital humain à travers des mesures de l’éducation en utilisant notamment la moyenne d’années de scolarisation (stock du capital humain). Notre base de données, qui présente une mesure alternative du capital humain, tend à améliorer sensiblement le mode de calcul des inégalités de l’éducation. Elle exploite toute la richesse des données désagrégées, corrige les pondérations inappropriées et affine certaines hypothèses réductrices sur les durées des cycles d’enseignement et les niveaux d’éducation retenus. Nous avons aussi généralisé la formule proposée par Berthélemy (2006) sur l’indice de Gini de l’éducation. Le domaine de variation possible de cet indice est identifié graphiquement selon la moyenne d’années de scolarisation et les durées cumulées des cycles d’enseignement. Nous mettons en évidence, dans le cadre du chapitre II, l’existence d’une relation non linéaire entre les inégalités dans l’éducation et le développement économique en utilisant des modèles non-paramétriques et semi-paramétriques qui n’exigent pas de formes fonctionnelles prédéfinies à l’avance. Plusieurs phases sont ainsi mises en évidence : les trois premières sont repérées seulement par rapport aux niveaux de développement ; deux autres sont identifiées à la fois par des seuils de développement et d’inégalité d’éducation ; une sixième et dernière phase est définie par rapport au seul niveau d’inégalité d’éducation. Nous montrons que c’est dans la troisième et cinquième phases que la réduction de l’inégalité d’éducation présente l’impact le plus bénéfique sur le développement économique.Au-delà du schéma général mis en évidence sur le plan transnational dans les chapitres I et II, nous explorons dans le chapitre III la nature de cette relation au plan régional dans le cas du Maroc, pour lequel nous disposons de données aux niveaux communal et provincial. La non-linéarité de la relation est aussi confirmée. La troisième phase repérée au chapitre II est subdivisée, dans le cas des provinces marocaines, en deux sous phases qui présentent un impact différencié selon un seuil de développement et d’inégalité d’éducation. / This thesis seeks to deepen the nature and the shape of the relationships between educational inequalities and development. It goes along with the prolongation of the analyses undertaken about the relationships between both education & growth; and inequality & growth, by trying to shed additional light on these two. It aims to retrace, in a schematic way, the evolution of educational inequalities particularly in the developing countries; and also to characterize the nonlinearity of this link using nonparametric and semiparametric estimation models.This thesis consists of three chapters that correspond to specific objectives, databases and methodologies. In the first chapter, we propose a new dataset on the inequalities of education. Most of the studies on the relationship between human capital and economic development have mainly apprehended the measurement of human capital through quantitative education indicators, using namely the average of years of schooling (human capital stock). Our database, which presents an alternative measure of human capital, tends to improve significantly the way in which inequalities in education are calculated. It employs all the abundance of disaggregated data, corrects inappropriate weightings and refines some reductive assumptions about the durations of schooling cycles and the levels of education. We have also generalized the formula proposed by Berthélemy (2006) on the Gini index of education. The possible variation range of this index is graphically identified according to the average years of schooling and the cumulative duration of the schooling cycles. In Chapter II, we reveal the existence of a nonlinear relationship between inequalities in education and economic development using nonparametric and semiparametric models that do not require predefined functional forms. Several phases are therefore highlighted: the first three are identified only according to the level of development; then two other phases are recognized by combining thresholds of both development and education inequality; the sixth and final phase is defined by the educational inequality level alone. We show that the phases during which the reduction of educational inequality presents the most beneficial impact on economic development are the third and the fifth.Beyond the general outline highlighted at the transnational level in Chapters I and II, we explore in Chapter III the nature of this relationship at the regional level in the case of Morocco, for which we have data at both the municipal and provincial levels. We also confirm the nonlinearity of the relationship. The third phase, identified in Chapter II, is divided to two sub-phases in the case of the Moroccan provinces which have a differentiated impact according to a threshold of development and inequality of education.

Series data, sequences of measured values, are ubiquitous. Whenever observations are made along a path in space or time, a data sequence results. To comprehend nature and shape it to our will, or to make informed decisions based on what we know, we need methods to make sense of such data. Of particular interest are probabilistic descriptions, which enable us to represent uncertainty and random variation inherent to the world around us. This thesis presents and expands upon some tools for creating probabilistic models of sequences, with an eye towards applications involving speech and language. Modelling speech and language is not only of use for creating listening, reading, talking, and writing machines---for instance allowing human-friendly interfaces to future computational intelligences and smart devices of today---but probabilistic models may also ultimately tell us something about ourselves and the world we occupy. The central theme of the thesis is the creation of new or improved models more appropriate for our intended applications, by weakening limiting and questionable assumptions made by standard modelling techniques. One contribution of this thesis examines causal-state splitting reconstruction (CSSR), an algorithm for learning discrete-valued sequence models whose states are minimal sufficient statistics for prediction. Unlike many traditional techniques, CSSR does not require the number of process states to be specified a priori, but builds a pattern vocabulary from data alone, making it applicable for language acquisition and the identification of stochastic grammars. A paper in the thesis shows that CSSR handles noise and errors expected in natural data poorly, but that the learner can be extended in a simple manner to yield more robust and stable results also in the presence of corruptions. Even when the complexities of language are put aside, challenges remain. The seemingly simple task of accurately describing human speech signals, so that natural synthetic speech can be generated, has proved difficult, as humans are highly attuned to what speech should sound like. Two papers in the thesis therefore study nonparametric techniques suitable for improved acoustic modelling of speech for synthesis applications. Each of the two papers targets a known-incorrect assumption of established methods, based on the hypothesis that nonparametric techniques can better represent and recreate essential characteristics of natural speech. In the first paper of the pair, Gaussian process dynamical models (GPDMs), nonlinear, continuous state-space dynamical models based on Gaussian processes, are shown to better replicate voiced speech, without traditional dynamical features or assumptions that cepstral parameters follow linear autoregressive processes. Additional dimensions of the state-space are able to represent other salient signal aspects such as prosodic variation. The second paper, meanwhile, introduces KDE-HMMs, asymptotically-consistent Markov models for continuous-valued data based on kernel density estimation, that additionally have been extended with a fixed-cardinality discrete hidden state. This construction is shown to provide improved probabilistic descriptions of nonlinear time series, compared to reference models from different paradigms. The hidden state can be used to control process output, making KDE-HMMs compelling as a probabilistic alternative to hybrid speech-synthesis approaches. A final paper of the thesis discusses how models can be improved even when one is restricted to a fundamentally imperfect model class. Minimum entropy rate simplification (MERS), an information-theoretic scheme for postprocessing models for generative applications involving both speech and text, is introduced. MERS reduces the entropy rate of a model while remaining as close as possible to the starting model. This is shown to produce simplified models that concentrate on the most common and characteristic behaviours, and provides a continuum of simplifications between the original model and zero-entropy, completely predictable output. As the tails of fitted distributions may be inflated by noise or empirical variability that a model has failed to capture, MERS's ability to concentrate on high-probability output is also demonstrated to be useful for denoising models trained on disturbed data. / <p>QC 20131128</p> / ACORNS: Acquisition of Communication and Recognition Skills / LISTA – The Listening Talker