In this thesis, we study the least trimmed squares artificial neural networks (LTS-ANNs), which are generalization of the least trimmed squares (LTS) estimators frequently used in robust linear parametric regression problems to nonparametric artificial neural networks (ANNs) used for nonlinear regression problems. Two training algorithms are proposed in this thesis. The first algorithm is the incremental gradient descent algorithm. In order to speed up the convergence, the second training algorithm is proposed based on recursive least squares (RLS). Three illustrative examples are provided to test the performances of robustness against outliers for the classical ANNs and the LTS-ANNs. Simulation results show that upon proper selection of the trimming constant of the learning machines, LTS-ANNs are quite robust against outliers compared with the classical ANNs.

Na década de 1990, emergiu uma numerosa literatura abordando os efeitos da confiança interpessoal no crescimento econômico dos países. Teoricamente, a confiança afeta o crescimento econômico por afetar as decisões que envolvem incerteza acerca das ações futuras de outros agentes, como: investimentos, contratações de trabalhadores, inovação, dentre outras. Este trabalho utiliza a metodologia corrente nesta literatura, avaliando o papel da confiança no crescimento econômico em um cross section de países para três períodos, utilizando informações, principalmente, das Penn World Tables, World Values Survey e dados de educação da UNESCO. Aplicando a técnica de least trimmed squares é avaliada a robustez da variável confiança quando se retiram observações aberrantes. Encontra-se que a confiança tem um efeito considerável no crescimento econômico, mesmo quando outliers são removidos. Também são realizados exercícios para a correção de possíveis problemas de endogeneidade da variável de confiança. Além disso, o trabalho analisa os determinantes da confiança individual, utilizando um modelo probit cujas variáveis explicativas são: renda, escolaridade, idade, país, religião, dentre outras. Este exercício também é feito para analisar o caso brasileiro. Encontra-se que a confiança é uma variável que depende mais da sociedade ou do grupo que das características individuais e, para o caso brasileiro, verificou-se que independentemente de gênero, escolaridade ou renda, as pessoas não confiam nos demais. / In the 1990\'s a large number of works came out investigating the effects of interpersonal trust on the economic growth of countries. Theoretically, trust affects economic growth by affecting all decisions that involve uncertainty on future actions of other agents, such as: investments, hire of employees, innovation, among others. This study uses the current literature methodology, tackling the trust importance for economic growth on a cross section of countries for three periods, using informations mainly from the Penn World Tables, World Values Survey and educational data from UNESCO. Applying the least trimmed squares technique it is evaluated the robustness of the trust variable when influential observations are excluded. It is found a remarkable estimated effect of trust on economic growth, even when outliers are removed. Also some studies are made in order to correct for possible endogeneity problems of the trust variable. Moreover, the work analyses the determinants of individual trust, using a probit model with the regressors: income, schooling, age, country, religion, among others. This analysis is also applied for the brazilian case. It is found that trust depends more on the society or group than on individual characteristics and, for the brazilian case, it was observed that, no matter which gender, schooling or income level the person belongs to, people do not trust each other.

Na década de 1990, emergiu uma numerosa literatura abordando os efeitos da confiança interpessoal no crescimento econômico dos países. Teoricamente, a confiança afeta o crescimento econômico por afetar as decisões que envolvem incerteza acerca das ações futuras de outros agentes, como: investimentos, contratações de trabalhadores, inovação, dentre outras. Este trabalho utiliza a metodologia corrente nesta literatura, avaliando o papel da confiança no crescimento econômico em um cross section de países para três períodos, utilizando informações, principalmente, das Penn World Tables, World Values Survey e dados de educação da UNESCO. Aplicando a técnica de least trimmed squares é avaliada a robustez da variável confiança quando se retiram observações aberrantes. Encontra-se que a confiança tem um efeito considerável no crescimento econômico, mesmo quando outliers são removidos. Também são realizados exercícios para a correção de possíveis problemas de endogeneidade da variável de confiança. Além disso, o trabalho analisa os determinantes da confiança individual, utilizando um modelo probit cujas variáveis explicativas são: renda, escolaridade, idade, país, religião, dentre outras. Este exercício também é feito para analisar o caso brasileiro. Encontra-se que a confiança é uma variável que depende mais da sociedade ou do grupo que das características individuais e, para o caso brasileiro, verificou-se que independentemente de gênero, escolaridade ou renda, as pessoas não confiam nos demais. / In the 1990\'s a large number of works came out investigating the effects of interpersonal trust on the economic growth of countries. Theoretically, trust affects economic growth by affecting all decisions that involve uncertainty on future actions of other agents, such as: investments, hire of employees, innovation, among others. This study uses the current literature methodology, tackling the trust importance for economic growth on a cross section of countries for three periods, using informations mainly from the Penn World Tables, World Values Survey and educational data from UNESCO. Applying the least trimmed squares technique it is evaluated the robustness of the trust variable when influential observations are excluded. It is found a remarkable estimated effect of trust on economic growth, even when outliers are removed. Also some studies are made in order to correct for possible endogeneity problems of the trust variable. Moreover, the work analyses the determinants of individual trust, using a probit model with the regressors: income, schooling, age, country, religion, among others. This analysis is also applied for the brazilian case. It is found that trust depends more on the society or group than on individual characteristics and, for the brazilian case, it was observed that, no matter which gender, schooling or income level the person belongs to, people do not trust each other.

In many practical applications, it is well known that data collected inevitably contain one or more anomalous outliers; that is, observations that are well separated from the majority or bulk of the data, or in some fashion deviate from the general pattern of the data. The occurrence of outliers may be due to misplaced decimal points, recording errors, transmission errors, or equipment failure. These outliers can lead to erroneous parameter estimation and consequently affect the correctness and accuracy of the model inference. In order to solve these problems, three robust fuzzy neural networks (FNNs) will be proposed in this dissertation. This provides alternative learning machines when faced with general nonlinear learning problems. Our emphasis will be put particularly on the robustness of these learning machines against outliers. Though we consider only FNNs in this study, the extension of our approach to other neural networks, such as artificial neural networks and radial basis function networks, is straightforward. In the first part of the dissertation, M-estimators, where M stands for maximum likelihood, frequently used in robust regression for linear parametric regression problems will be generalized to nonparametric Maximum Likelihood Fuzzy Neural Networks (MFNNs) for nonlinear regression problems. Simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) will be derived. In the second part of the dissertation, least trimmed squares estimators, abbreviated as LTS-estimators, frequently used in robust (or resistant) regression for linear parametric regression problems will be generalized to nonparametric least trimmed squares fuzzy neural networks, abbreviated as LTS-FNNs, for nonlinear regression problems. Again, simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) algorithms will be provided. In the last part of the dissertation, by combining the easy interpretability of the parametric models and the flexibility of the nonparametric models, semiparametric fuzzy neural networks (semiparametric FNNs) and semiparametric Wilcoxon fuzzy neural networks (semiparametric WFNNs) will be proposed. The corresponding learning rules are based on the backfitting procedure which is frequently used in semiparametric regression.

The ordinary least squares (OLS) is one of the most widely used methods for modelling the functional relationship between variables. However, this estimation procedure counts on some assumptions and the violation of these assumptions may lead to nonrobust estimates. In this study, the simple linear regression model is investigated for conditions in which the distribution of the error terms is Generalised Logistic. Some robust and nonparametric methods such as modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares, least trimmed squares (LTS), Theil and weighted Theil are compared via computer simulation. In order to evaluate the estimator performance, mean, variance, bias, mean square error (MSE) and relative mean square error (RMSE) are computed.

資本資產定價模型 (CAPM) 由Sharp (1964)、Lintner (1965)及Black (1972)發展出後，近年來已被廣泛的應用於衡量證券之預期報酬率與風險間之關係。一般而言，衡量結果之估計有兩個階段，首先由時間序列分析估計出貝它(beta)係數，然後再檢定廠商或投資組合之平均報酬率與貝它係數之關係。 Fama與MacBeth (1973)利用最小平方法估計貝它係數，再將由橫斷面迴歸方法所得出之斜率係數加以平均後，以統計t-test檢定之。然而以最小平方法估計係數，其估計值很容易受離群值之影響，因此本研究考慮以穩健估計 (robust estimator)來避免此一問題。另外，本研究亦將長期資料分析 (longitudinal data analysis) 引入CAPM裡，期望能檢定貝它係數是否能確實有效地衡量出系統性風險。 論文中以台灣股票市場電子業之實證分析來比較上述不同方法對CAPM的結果，資料蒐集期間為1998年9月至2001年12月之月資料。研究結果顯示出，穩健估計相對於最小平方法就CAPM有較佳的解釋力。而長期資料分析模型更用來衡量債券之超額報酬部分，是否會依上、中、下游或公司之不同而不同。 / The Capital Asset Pricing Model (CAPM) of Sharp (1964), Lintner (1965) and Black (1972) has been widely used in measuring the relationship between the expected return on a security and its risk in the recent years. It consists of two stages to estimate the relationship between risk and expected return. The first one is that betas are estimated from time series regressions, and the second is that the relationship between mean returns and betas is tested across firms or portfolios. Fama and MacBeth (1973) first used ordinary least squares (OLS) to estimate beta and took time series averages of the slope coefficients from monthly cross-sectional regressions in such studies. However it is well known that OLS is sensitive to outliers. Therefore, robust estimators are employed to avoid the problems. Furthermore, the longitudinal data analysis is applied to examine whether betas over time and securities are the valid measure of risk in the CAPM. An empirical study is carried out to present the different approaches. We use the data about the Information and Electronic industry in Taiwan stock market during the period from September 1998 to December 2001. For the time series regression analysis, the robust methods lead to more explanatory power than the OLS results. The linear mixed-effect model is used to examine the effects of different streams and companies for the security excess returns in these data.

在傳統的線性迴歸分析當中，當基本假設不滿足時，有時可考慮變數轉換使得資料能夠比較符合基本假設。在眾多的轉換方法當中，以Box和Cox(1964)所提出的乘冪轉換(Box-Cox power transformation)最為常用，乘冪轉換可將某些複雜的系統轉換成線性常態模式。然而當資料存在離群值(outlier)時，Box-Cox Transformation會受到影響，因此不是一種穩健方法。 在本篇論文當中，我們利用前進演算法(forward search algorithm)求得最小消去平方估計量(Least trimmed squares estimator)，在過程當中估計出穩健的轉換參數。