<p>Quantile regression have its advantage properties comparing to the OLS model regression which are full measurement of the effects of a covariate on response, robustness and Equivariance property. In this paper, I use a survey data in Belgium and apply a linear model to see the advantage properites of quantile regression. And I use a quantile regression model with the raw data to analyze the different cost of family on different numbers of children and apply a Wald test. The result shows that for most of the family types and living standard, from the lower quantile to the upper quantile the family cost on children increases along with the increasing number of children and the cost of each child is the same. And we found a common behavior that the cost of the second child is significantly more than the cost of the first child for a nonworking type of family and all living standard families, at the upper quantile (from 0.75 quantile to 0.9 quantile) of the conditional distribution.</p>

Quantile regression have its advantage properties comparing to the OLS model regression which are full measurement of the effects of a covariate on response, robustness and Equivariance property. In this paper, I use a survey data in Belgium and apply a linear model to see the advantage properites of quantile regression. And I use a quantile regression model with the raw data to analyze the different cost of family on different numbers of children and apply a Wald test. The result shows that for most of the family types and living standard, from the lower quantile to the upper quantile the family cost on children increases along with the increasing number of children and the cost of each child is the same. And we found a common behavior that the cost of the second child is significantly more than the cost of the first child for a nonworking type of family and all living standard families, at the upper quantile (from 0.75 quantile to 0.9 quantile) of the conditional distribution.

Gegenstand dieser Arbeit ist die Betrachtung verschiedener Likelihoodquotiententest für weibullverteilte Grundgesamtheiten. Zunächst wird der Likelihoodquotiententest mit festem Stichprobenumfang zum Prüfen des Formparameters der Weibullverteilung betrachtet, der zwischen zwei Hypothesen entscheidet. Da eine Beobachtung stetiger Zufallsgrößen in der Praxis nur in eingeschränktem Maße möglich ist, wird nach einer allgemeinen Beschreibung des Tests zu einem Likelihoodquotiententest mit gruppierten Beobachtungen übergegangen. Durch eine Verallgemeinerung des Likelihoodquotiententests mit festem Stichprobenumfang wird der sequentielle Quotiententest eingeführt, wobei nun der Stichprobenumfang eine Zufallsgröße ist. Häufig ist es erwünscht, dass ein Test nicht nur zwischen zwei Hypothesen entscheidet, sondern zwischen mehreren Hypothesen. Dieses Mehrentscheidungsproblem wird anhand des Sobel-Wald-Tests in der vorliegenden Arbeit betrachtet, dabei wird sich auf die Betrachtung von drei Hypothesen zurückgezogen. Neben der Betrachtung der Operationscharakteristiken und des mittleren Stichprobenumfangs für diese Tests, wird zudem untersucht, wie sich diese Charakteristiken bei verschiedenen Parameterkonstellationen ändern.

Gegenstand dieser Arbeit ist die Betrachtung verschiedener Likelihoodquotiententest für weibullverteilte Grundgesamtheiten. Zunächst wird der Likelihoodquotiententest mit festem Stichprobenumfang zum Prüfen des Formparameters der Weibullverteilung betrachtet, der zwischen zwei Hypothesen entscheidet. Da eine Beobachtung stetiger Zufallsgrößen in der Praxis nur in eingeschränktem Maße möglich ist, wird nach einer allgemeinen Beschreibung des Tests zu einem Likelihoodquotiententest mit gruppierten Beobachtungen übergegangen. Durch eine Verallgemeinerung des Likelihoodquotiententests mit festem Stichprobenumfang wird der sequentielle Quotiententest eingeführt, wobei nun der Stichprobenumfang eine Zufallsgröße ist. Häufig ist es erwünscht, dass ein Test nicht nur zwischen zwei Hypothesen entscheidet, sondern zwischen mehreren Hypothesen. Dieses Mehrentscheidungsproblem wird anhand des Sobel-Wald-Tests in der vorliegenden Arbeit betrachtet, dabei wird sich auf die Betrachtung von drei Hypothesen zurückgezogen. Neben der Betrachtung der Operationscharakteristiken und des mittleren Stichprobenumfangs für diese Tests, wird zudem untersucht, wie sich diese Charakteristiken bei verschiedenen Parameterkonstellationen ändern.

Submitted by joao barbosa campbell penna (joao.penna@vale.com) on 2015-02-20T19:44:37Z No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2015-06-08T18:42:08Z (GMT) No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-06-12T17:55:33Z (GMT) No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) / Made available in DSpace on 2015-06-12T17:56:53Z (GMT). No. of bitstreams: 1 TESEFINAL_20022015.pdf: 1480842 bytes, checksum: 11e3f73bc5b243b7ed4a73b63fe90c59 (MD5) Previous issue date: 2014-12-20 / Medimos a validade da paridade descoberta de juros – PDJ - para o mercado brasileiro no período de janeiro de 2010 a julho de 2014. Testamos a equação clássica da PDJ usando o Método dos Mínimos Quadrados Ordinários. Após a estimação dos parâmetros, aplicamos o Teste de Wald e verificamos que a paridade descoberta de juros não foi validada. Estendemos a equação tradicional da PDJ para uma especificação alternativa que captura medidas de risco Brasil e de alteração na liquidez internacional. Especificamente, acrescentamos três variáveis de controle: duas variáveis dummy que capturam condições de liquidez externa e o índice de commoditie CRB, que captura o risco Brasil. Com a especificação alternativa, a hipótese de que os retornos das taxas de juros em Real, dolarizadas, são iguais aos retornos da taxas de juros contratadas em dólares, ambas sujeitas ao risco Brasil, não foi rejeitada. Em complemento à análise das taxas representativas do mercado brasileiro, procurou-se avaliar a predominância da PDJ nas operações de swap cambial realizadas pela Vale S.A.. Para tanto, a série de taxa de juros em dólares do mercado brasileiro foi substituída pela taxa em dólar dos swaps contratados pela Vale. Os resultados encontrados demonstram que, quando comparado ao comportamento do mercado, as taxas em dólares da VALE são mais sensíveis às variações das taxas em Reais. / We measure the validity of uncovered interest parity - UIP - for the Brazilian market from January, 2010 to July, 2014. We tested the classical equation of UIP using the ordinary least squares method. After the estimation, we apply the Wald test and we verify that the uncovered interest parity has not been validated. We extend the traditional UIP equation for an alternative specification that captures Brazil risk and changes in liquidity of the international market. Specifically, we add three control variables: two dummy variables that capture external liquidity conditions and the commodity index CRB, which captures Brazil risk. With the alternative specification, the hypothesis that the returns in interest rates in Real, dollarized, are equal to the return of interest rate contracted in dollars, both subject to Brazil risk, was not rejected. To complement the analysis using the interest rates existing in the Brazilian market, we tried to evaluate the prevalence of UIP in cross currency interest rate swaps carried out by Vale SA. The interest rate in dollar of the Brazilian market was replaced by the dollar rate of swaps contracted by Vale. The results show that, when compared to market behavior, the dollar rates of Vale SA. are more sensitive to changes in Reais interest rates.

This thesis concentrates on regression models with a categorical response. It focuses on the model of logistic regression with binary response and its generalization in which two models are distinguished: multinomial regression with nominal response and multinomial regression with ordinal response. For all three models separately, the Wald test and the likelihood ratio test are derived. These theoretical derivations are then used to calculate the test statistics for specific examples in statistical software R. The theory described in the thesis is illustrated by examples with small and large number of explanatory variables.

No description available.

No description available.

This thesis investigates the factors that are associated with annual changes in the share price of Johannesburg Stock Exchange (JSE) listed companies. In this study, an increase in value of a share is when the share price of a company goes up by the end of the financial year as compared to the previous year. Secondary data that was sourced from McGregor BFA website was used. The data was from 2004 up to 2011. Deciding which share to buy is the biggest challenge faced by both investment companies and individuals when investing on the stock exchange. This thesis uses binary logistic regression to identify the variables that are associated with share price increase. The dependent variable was annual change in share price (ACSP) and the independent variables were assets per capital employed ratio, debt per assets ratio, debt per equity ratio, dividend yield, earnings per share, earnings yield, operating profit margin, price earnings ratio, return on assets, return on equity and return on capital employed. Different variable selection methods were used and it was established that the backward elimination method produced the best model. It was established that the probability of success of a share is higher if the shareholders are anticipating a higher return on capital employed, and high earnings/ share. It was however, noted that the share price is negatively impacted by dividend yield and earnings yield. Since the odds of an increase in share price is higher if there is a higher return on capital employed and high earning per share, investors and investment companies are encouraged to choose companies with high earnings per share and the best returns on capital employed. The final model had a classification rate of 68.3% and the validation sample produced a classification rate of 65.2% / Mathematical Sciences / M.Sc. (Statistics)

Para analisar características de interesse a respeito de um conjunto de dados reais da área de Odontologia apresentado em Hadgu & Koch (1999), ajustaremos um modelo de regressão linear multivariado com erros nas variáveis com intercepto nulo. Este conjunto de dados é caracterizado por medições de placa bacteriana em três grupos de voluntários, antes e após utilizar dois líquidos de bochecho experimentais e um líquido de bochecho controle, com medições (sujeitas a erros de medição) no início do estudo, após três e seis meses de utilização dos líquidos. Neste caso, uma possível estrutura de dependência entre as medições feitas em um mesmo indivíduo deve ser incorporada ao modelo e, além disto, temos duas variáveis resposta para cada indivíduo. Após a apresentação do modelo estatístico, iremos obter estimativas de máxima verossimilhança dos parâmetros utilizando o algoritmo iterativo EM e testaremos as hipóteses de interesse utilizando testes assintóticos de Wald, razão de verossimilhanças e score. Como neste caso não existe um teste ótimo, faremos um estudo de simulação para verificar o comportamento das três estatísticas de teste em relação a diferentes tamanhos amostrais e diferentes valores de parâmetros. Finalmente, faremos um estudo de diagnóstico buscando identificar possíveis pontos influentes no modelo, considerando o enfoque de influência local proposto por Cook (1986) e a medida de curvatura normal conformal desenvolvida por Poon & Poon (1999). / To analyze some characteristics of interest in a real odontological data set presented in Hadgu & Koch (1999), we propose the use of a multivariate null intercept errors-in-variables regression model. This data set is composed by measurements of dental plaque index (with measurement errors), which were measured in volunteers who were randomized to two experimental mouth rinses (A and B) or a control mouth rinse. The measurements were taken in each individual, before and after the use of the respective mouth rinses, in the beginning of the study, after three months from the baseline and after six months from the baseline. In this case, a possible structure of dependency between the measurements taken within the same individual must be incorporated in the model. After presenting the statistical model, we obtain the maximum likelihood estimates of the parameters using the numerical algorithm EM, and we test the hypotheses of interest considering asymptotic tests (Wald, likelihood ratio and score). Also, a simulation study to verify the behavior of these three test statistics is presented, considering diferent sample sizes and diferent values for the parameters. Finally, we make a diagnostic study to identify possible influential observations in the model, considering the local influence approach proposed by Cook (1986) and the conformal normal curvature proposed by Poon & Poon (1999).