Many minimum distance estimators have the potential to provide parameter estimates which are both robust and efficient and yet, despite these highly desirable theoretical properties, they are rarely used in practice. This is because the performance of these estimators is rarely guaranteed per se but obtained by placing a suitable value on some tuning parameter. Hence there is a risk involved in implementing these methods because if the value chosen for the tuning parameter is inappropriate for the data to which the method is applied, the resulting estimators may not have the desired theoretical properties and could even perform less well than one of the simpler, more widely used alternatives. There are currently no data-based methods available for deciding what value one should place on these tuning parameters hence the primary aim of this research is to develop an objective way of selecting values for the tuning parameters in minimum distance estimators so that the full potential of these estimators might be realised. This new method was initially developed to optimise the performance of the density power divergence estimator, which was proposed by Basu, Harris, Hjort and Jones [3]. The results were very promising so the method was then applied to two other minimum distance estimators and the results compared.

Ever since the pioneering work of Parzen the mean square error( MSE) and its integrated form (MISE) have been used as the error criteria in choosing the bandwidth matrix for multivariate kernel density estimation. More recently other criteria have been advocated as competitors to the MISE, such as the mean absolute error. In this study we define a weighted version of the Hellinger distance for multivariate densities and show that it has an asymptotic form, which is one-fourth the asymptotic MISE under weak smoothness conditions on the multivariate density f. In addition the proposed criteria give rise to a new data-dependent bandwidth matrix selector. The performance of the new data-dependent bandwidth matrix selector is compared with other well known bandwidth matrix selectors such as the least squared cross validation (LSCV) and the plug-in (HPI) through simulation. We derived a closed form formula for the mean Hellinger distance (MHD) in the univariate case. We also compared via simulation mean weighted Hellinger distance (MWHD) and the asymptotic MWHD, and the MISE and the asymptotic MISE for both univariate and bivariate cases for various densities and sample sizes.

The theme of providing predictable criteria for absolute continuity and for mutual singularity of two density processes on a filtered probability space is extensively studied, e.g., in the monograph by J. Jacod and A. N. Shiryaev [JS]. While the issue of absolute continuity is settled there in full generality, for the issue of mutual singularity one technical difficulty remained open ([JS], p210): "We do not know whether it is possible to derive a predictable criterion (necessary and sufficient condition) for "P'T..." (expression not representable in this abstract). It turns out that to this question raised in [JS] which we also chose as the title of this note, there are two answers: on the negative side we give an easy example, showing that in general the answer is no, even when we use a rather wide interpretation of the concept of "predictable criterion". The difficulty comes from the fact that the density process of a probability measure P with respect to another measure P' may suddenly jump to zero. On the positive side we can characterize the set, where P' becomes singular with respect to P - provided this does not happen in a sudden but rather in a continuous way - as the set where the Hellinger process diverges, which certainly is a "predictable criterion". This theorem extends results in the book of J. Jacod and A. N. Shiryaev [JS]. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Robust estimation of statistical parameters is traditionally believed to exist in a trade space between robustness and efficiency. This thesis examines the Minimum Hellinger Distance Estimator (MHDE), which is known to have desirable robustness properties as well as desirable efficiency properties. This thesis confirms that the MHDE is simultaneously robust against outliers and asymptotically efficient in the univariate location case. Robustness results are then extended to the case of simple linear regression, where the MHDE is shown empirically to have a breakdown point of 50%. A geometric algorithm for solution of the MHDE is developed and implemented. The algorithm utilizes the Riemannian manifold properties of the statistical model to achieve an algorithmic speedup. The MHDE is then applied to an illustrative problem in power system state estimation. The power system is modeled as a structured linear regression problem via a linearized direct current model; robustness results in this context have been investigated and future research areas have been identified from both a statistical perspective as well as an algorithm design standpoint. / Master of Science

Master of Science / Department of Statistics / Weixin Yao / In this report, we introduce the minimum Hellinger distance (MHD) estimation method and review its history. We examine the use of Hellinger distance to obtain a new efficient and robust estimator for a class of semiparametric mixture models where one component has known distribution while the other component and the mixing proportion are unknown. Such semiparametric mixture models have been used in biology and the sequential clustering algorithm. Our new estimate is based on the MHD, which has been shown to have good efficiency and robustness properties. We use simulation studies to illustrate the finite sample performance of the proposed estimate and compare it to some other existing approaches. Our empirical studies demonstrate that the proposed minimum Hellinger distance estimator (MHDE) works at least as well as some existing estimators for most of the examples considered and outperforms the existing estimators when the data are under contamination. A real data set application is also provided to illustrate the effectiveness of our proposed methodology.

Submitted by Marilene Donadel (marilene.donadel@unioeste.br) on 2019-01-23T18:30:18Z No. of bitstreams: 1 Renata_Saldanha_2018.pdf: 810101 bytes, checksum: b45ce79ad809216543b1f4f2228e57f1 (MD5) / Made available in DSpace on 2019-01-23T18:30:18Z (GMT). No. of bitstreams: 1 Renata_Saldanha_2018.pdf: 810101 bytes, checksum: b45ce79ad809216543b1f4f2228e57f1 (MD5) Previous issue date: 2018-08-31 / This dissertation aims to analyze Restorative Justice and its practices, to find a meeting point for the foundation of these practices in Philosophy, especially based on the systemic-phenomenological theory of Bert Hellinger. Restorative Justice is a relatively new topic in Brazil and it has been increasingly used, but it is still needy the study of this subject when is not under a practical bias. Thus, this work seeks to conceptualize the theme based on the bibliographical review on the subject, with Kant, Hegel and Bert Hellinger. In the first chapter, the context of the flowering of restorative practices in Brazil, with a focus on the criminal area and the essentiality of its theory, is worked on: new vision of conflict, inclusion, participation, (co) responsibility, voluntariness, honesty, humility, interconnection, empowerment, hope, solidarity and the encounter. In the second chapter, Restorative Justice is approached from a critical perspective, especially on the basis of Kant and Hegel, the main framers of the current model of retributive justice.For Kant, crime is the non-fulfillment of a duty and punishment is a punishment for such an action, that is, punishment is the retribution of the evil of crime with the evil of pen, in a strictly formal paradigm. In Hegel, law is the most accurate form of law and its violation hurts the highest degree of human freedom. The Law defines the duties and the rights of the subjects. Duty is negative determination and right is positive determination of freedom. But since law and duty can be denied, law internalizes its own negation, so that this negation is not formally infinite. Thus, the denial of law by the law itself is the sanction, which also denotes a formalist bias of the concept of justice and punishment. Finally, in the last chapter, and after locating the central elements of restorative practices, we seek in Bert Hellinger's systemic-phenomenological theory a foundation for restorative practices. Bert Hellinger supposes that there are three laws that govern all human relationships: belonging, hierarchy and balance. As every system values inclusiveness, belonging is the right of everyone to be part of it. Hierarchy is the order of precedence of people as time passes. Finally, balance is the trade-off between giving and taking, representing a flow of exchange that animates human relationships. The major point of contact between restorative practices and the systemic-phenomenological theory is the change of perception in relation to the conflict, with the inclusion, which derives from the right to belong, the equality, the dignity of the human person, which makes reconciliation possible and opens the way to peace, enabling, in turn, the construction of the sense of justice. concluding that Restorative Justice is a meeting with itself and with the other, face-to-face, aiming to understand the hidden causes and entanglements which led to conflict in a larger context (beyond the conflict), with the assumption of the responsibility of each one to the event of the conflict and construction of the systemic reparation of damages (material, spiritual, emotional, transgenerational, psychological, symbolic). Bert Hellinger's theory allows us to transcend the differentiations that exclude and restore the basic human need for connection with other human beings. / Esta dissertação tem por objetivo analisar a Justiça Restaurativa e suas práticas e encontrar um ponto de encontro para a fundamentação destas práticas na Filosofia, especialmente com base na teoria sistêmico-fenomenológica de Bert Hellinger. A Justiça Restaurativa é um tema relativamente novo no Brasil e ela vem sendo cada vez mais utilizada, mas ainda é carente o estudo desse tema que não seja sob um viés prático. Assim, este trabalho busca conceituar o tema com base na revisão bibliográfica sobre o assunto, com apoio na filosofia de Kant, Hegel e Bert Hellinger. No primeiro capítulo, é trabalhado o contexto de florescimento das práticas restaurativas no Brasil, com enfoque na área criminal e a essencialidade de sua teoria: nova visão do conflito, inclusão, participação, (co)responsabilidade, voluntariedade, honestidade, humildade, interconexão, empoderamento, esperança, solidariedade e o encontro. No segundo capítulo, a Justiça Restaurativa é abordada sob uma perspectiva crítica, especialmente com base em Kant e Hegel, principais estruturadores do modelo de justiça retributivo vigente. Para Kant, o crime é o descumprimento de um dever e a punição é um castigo para tal ação, ou seja, a punição é a retribuição do mal do crime com o mal da pena, em um paradigma estritamente formal. Em Hegel, a lei constitui a forma mais apurada do Direito e sua violação fere o mais alto grau da liberdade humano. O Direito define os deveres e os direitos dos sujeitos. O dever é determinação negativa e o direito é determinação positiva da liberdade. Mas como o direito e o dever podem ser negados, o Direito interioriza sua própria negação, a fim de que essa negação não seja formalmente infinita. Assim, a negação do Direito pelo próprio Direito é a sanção, o que denota também um viés formalista do conceito de Justiça e punição. Por fim, no último capítulo, e após situar os elementos centrais das práticas restaurativas, busca-se na teoria sistêmico-fenomenológica de Bert Hellinger uma fundamentação para as práticas restaurativas. Bert Hellinger supõe que existem três leis que regem todos os relacionamentos humanos: o pertencimento, a hierarquia e o equilíbrio. Como todo sistema preza pela inclusão, o pertencimento é o direito de todos de fazerem parte. A hierarquia é a ordem de precedência das pessoas conforme o passar do tempo. Por fim, o equilíbrio é a compensação entre o dar e o tomar, representando um fluxo de troca que anima as relações humanas. O maior ponto de contato entre as práticas restaurativas e a teoria sistêmico-fenomenológica é a mudança de percepção em relação ao conflito, com a inclusão, que decorre do direito de pertencer, a igualdade, a dignidade da pessoa humana, o que possibilita a reconciliação e abre o caminho para a paz, possibilitando, por sua vez, a construção do sentido de Justiça. A Justiça Restaurativa assim representa um encontro consigo próprio e com o outro, face-a-face, visando compreender as causas ocultas e emaranhamentos que levaram ao conflito diante de um contexto maior (para além do conflito), com a assunção da responsabilidade de cada um para o acontecimento do conflito e construção da reparação sistêmica dos danos (material, espiritual, emocional, transgeracional, psicológico, simbólico). A teoria de Bert Hellinger permite transcender as diferenciações que excluem e restaurar a necessidade humana básica de conexão com os demais seres humanos.

In this dissertation, robust and efficient alternatives to quasi-likelihood estimation and likelihood ratio tests are developed for discrete generalized linear models. The estimation method considered is a penalized minimum Hellinger distance procedure that generalizes a procedure developed by Harris and Basu for estimating parameters of a single discrete probability distribution from a random sample. A bootstrap algorithm is proposed to select the weight of the penalty term. Simulations are carried out to compare the new estimators with quasi-likelihood estimation. The robustness of the estimation procedure is demonstrated by simulation work and by Hapel's α-influence curve. Penalized minimum Hellinger deviance tests for goodness-of-fit and for testing nested linear hypotheses are proposed and simulated. A nonparametric bootstrap algorithm is proposed to obtain critical values for the testing procedure.

No description available.

O objetivo deste trabalho é investigar o desempenho de estimadores baseados em momentos das famílias verossimilhança empírica generalizada (GEL) e mínimo contraste generalizado (GMC) na estimação de modelos de equilíbrio geral dinâmico e estocástico (DSGE), com enfoque na análise de robustez sob má-especificação, recorrente neste tipo de modelo. Como benchmark utilizamos método do momentos generalizado (GMM), máxima verossimilhança (ML) e inferência bayesiana (BI). Trabalhamos com um modelo de ciclos reais de negócios (RBC) que pode ser considerado o núcleo de modelos DSGE, apresenta dificuldades similares e facilita a análise dos resultados devido ao menor número de parâmetros. Verificamos por meio de experimentos de Monte Carlo se os estimadores estudados entregam resultados satisfatórios em termos de média, mediana, viés, erro quadrático médio, erro absoluto médio e verificamos a distribuição das estimativas geradas por cada estimador. Dentre os principais resultados estão: (i) o estimador verossimilhança empírica (EL) - assim como sua versão com condições de momento suavizadas (SEL) - e a inferência bayesiana (BI) foram, nesta ordem, os que obtiveram os melhores desempenhos, inclusive nos casos de especificação incorreta; (ii) os estimadores continous updating empirical likelihood (CUE), mínima distância de Hellinger (HD), exponential tilting (ET) e suas versões suavizadas apresentaram desempenho comparativo intermediário; (iii) o desempenho dos estimadores exponentially tilted empirical likelihood (ETEL), exponential tilting Hellinger distance (ETHD) e suas versões suavizadas foi bastante comprometido pela ocorrência de estimativas atípicas; (iv) as versões com e sem suavização das condições de momento dos estimadores das famílias GEL/GMC apresentaram desempenhos muito similares; (v) os estimadores GMM, principalmente no caso sobreidentificado, e ML apresentaram desempenhos consideravelmente abaixo de boa parte de seus concorrentes / The objective of this work is to investigate the performance of moment-based estimators of the generalized empirical likelihood (GEL) and generalized minimum contrast (GMC) families in the estimation of dynamic stochastic general equilibrium (DSGE) models, focusing on the robustness analysis under misspecification, recurrent in this model. As benchmark we used generalized method of moments (GMM), maximum likelihood (ML) and Bayesian inference (BI). We work with a real business cycle (RBC) model that can be considered the core of DSGE models, presents similar difficulties and facilitates the analysis of results due to lower number of parameters. We verified, via Monte Carlo experiments, whether the studied estimators presented satisfactory results in terms of mean, median, bias, mean square error, mean absolute error and we verified the distribution of the estimates generated by each estimator. Among the main results are: (i) empirical likelihood (EL) estimator - as well as its version with smoothed moment conditions (SEL) - and Bayesian inference (BI) were, in that order, the ones that obtained the best performances, even in misspecification cases; (ii) continuous updating empirical likelihood (CUE), minimum Hellinger distance (HD), exponential tilting (ET) estimators and their smoothed versions exhibit intermediate comparative performance; (iii) performance of exponentially tilted empirical likelihood (ETEL), exponential tilting Hellinger distance (ETHD) and its smoothed versions was seriously compromised by atypical estimates; (iv) smoothed and non-smoothed GEL/GMC estimators exhibit very similar performances; (v) GMM, especially in the over-identified case, and ML estimators had lower performance than their competitors

O objetivo deste trabalho é investigar o desempenho de estimadores baseados em momentos das famílias verossimilhança empírica generalizada (GEL) e mínimo contraste generalizado (GMC) na estimação de modelos de equilíbrio geral dinâmico e estocástico (DSGE), com enfoque na análise de robustez sob má-especificação, recorrente neste tipo de modelo. Como benchmark utilizamos método do momentos generalizado (GMM), máxima verossimilhança (ML) e inferência bayesiana (BI). Trabalhamos com um modelo de ciclos reais de negócios (RBC) que pode ser considerado o núcleo de modelos DSGE, apresenta dificuldades similares e facilita a análise dos resultados devido ao menor número de parâmetros. Verificamos por meio de experimentos de Monte Carlo se os estimadores estudados entregam resultados satisfatórios em termos de média, mediana, viés, erro quadrático médio, erro absoluto médio e verificamos a distribuição das estimativas geradas por cada estimador. Dentre os principais resultados estão: (i) o estimador verossimilhança empírica (EL) - assim como sua versão com condições de momento suavizadas (SEL) - e a inferência bayesiana (BI) foram, nesta ordem, os que obtiveram os melhores desempenhos, inclusive nos casos de especificação incorreta; (ii) os estimadores continous updating empirical likelihood (CUE), mínima distância de Hellinger (HD), exponential tilting (ET) e suas versões suavizadas apresentaram desempenho comparativo intermediário; (iii) o desempenho dos estimadores exponentially tilted empirical likelihood (ETEL), exponential tilting Hellinger distance (ETHD) e suas versões suavizadas foi bastante comprometido pela ocorrência de estimativas atípicas; (iv) as versões com e sem suavização das condições de momento dos estimadores das famílias GEL/GMC apresentaram desempenhos muito similares; (v) os estimadores GMM, principalmente no caso sobreidentificado, e ML apresentaram desempenhos consideravelmente abaixo de boa parte de seus concorrentes / The objective of this work is to investigate the performance of moment-based estimators of the generalized empirical likelihood (GEL) and generalized minimum contrast (GMC) families in the estimation of dynamic stochastic general equilibrium (DSGE) models, focusing on the robustness analysis under misspecification, recurrent in this model. As benchmark we used generalized method of moments (GMM), maximum likelihood (ML) and Bayesian inference (BI). We work with a real business cycle (RBC) model that can be considered the core of DSGE models, presents similar difficulties and facilitates the analysis of results due to lower number of parameters. We verified, via Monte Carlo experiments, whether the studied estimators presented satisfactory results in terms of mean, median, bias, mean square error, mean absolute error and we verified the distribution of the estimates generated by each estimator. Among the main results are: (i) empirical likelihood (EL) estimator - as well as its version with smoothed moment conditions (SEL) - and Bayesian inference (BI) were, in that order, the ones that obtained the best performances, even in misspecification cases; (ii) continuous updating empirical likelihood (CUE), minimum Hellinger distance (HD), exponential tilting (ET) estimators and their smoothed versions exhibit intermediate comparative performance; (iii) performance of exponentially tilted empirical likelihood (ETEL), exponential tilting Hellinger distance (ETHD) and its smoothed versions was seriously compromised by atypical estimates; (iv) smoothed and non-smoothed GEL/GMC estimators exhibit very similar performances; (v) GMM, especially in the over-identified case, and ML estimators had lower performance than their competitors