The Riemann-Hilbert method applied to the theory of orthogonal polynomials

Doutoramento em Matemática

Contributions to the theory of maximum entropy estimation for ill-posed models

As técnicas estatísticas são fundamentais em ciência e a análise de regressão linear é, quiçá, uma das metodologias mais usadas. É bem conhecido da literatura que, sob determinadas condições, a regressão linear é uma ferramenta estatística poderosíssima. Infelizmente, na prática, algumas dessas condições raramente são satisfeitas e os modelos de regressão tornam-se mal-postos, inviabilizando, assim, a aplicação dos tradicionais métodos de estimação. Este trabalho apresenta algumas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, em particular na estimação de modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. A investigação é desenvolvida em três vertentes, nomeadamente na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, na estimação do parâmetro ridge em regressão ridge e, por último, em novos desenvolvimentos na estimação com máxima entropia. Na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, o trabalho desenvolvido evidencia um melhor desempenho dos estimadores de máxima entropia em relação ao estimador de máxima verosimilhança. Este bom desempenho é notório em modelos com poucas observações por estado e em modelos com um grande número de estados, os quais são comummente afetados por colinearidade. Espera-se que a utilização de estimadores de máxima entropia contribua para o tão desejado aumento de trabalho empírico com estas fronteiras de produção. Em regressão ridge o maior desafio é a estimação do parâmetro ridge. Embora existam inúmeros procedimentos disponíveis na literatura, a verdade é que não existe nenhum que supere todos os outros. Neste trabalho é proposto um novo estimador do parâmetro ridge, que combina a análise do traço ridge e a estimação com máxima entropia. Os resultados obtidos nos estudos de simulação sugerem que este novo estimador é um dos melhores procedimentos existentes na literatura para a estimação do parâmetro ridge. O estimador de máxima entropia de Leuven é baseado no método dos mínimos quadrados, na entropia de Shannon e em conceitos da eletrodinâmica quântica. Este estimador suplanta a principal crítica apontada ao estimador de máxima entropia generalizada, uma vez que prescinde dos suportes para os parâmetros e erros do modelo de regressão. Neste trabalho são apresentadas novas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, tendo por base o estimador de máxima entropia de Leuven, a teoria da informação e a regressão robusta. Os estimadores desenvolvidos revelam um bom desempenho em modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. Por último, são apresentados alguns códigos computacionais para estimação com máxima entropia, contribuindo, deste modo, para um aumento dos escassos recursos computacionais atualmente disponíveis.

A Influência da personalidade e da sintomatologia na Theory of Mind

Dissertação de mestrado, Psicologia Clínica e da Saúde, Faculdade de Ciências Humanas e Sociais, Universidade do Algarve, 2015

The Impact of Thought Speed and Variability on Psychological State and Threat Perception: Further Exploration of the Theory of Mental Motion

Thought speed and variability are purportedly common features of specific psychological states, such as mania and anxiety. The present study explored the independent and combinational influence of these variables upon condition-specific symptoms and affective state, as proposed by Pronin and Jacobs’ (Perspect Psychol Sci, 3:461–485, 2008) theory of mental motion. A general population sample was recruited online (N = 263). Participants completed a thought speed and variability manipulation task, inducing a combination of fast/slow and varied/repetitive thought. Change in mania and anxiety symptoms was assessed through direct self-reported symptom levels and indirect, processing bias assessment (threat interpretation). Results indicated that fast and varied thought independently increased self-reported mania symptoms. Affect was significantly less positive and more negative during slow thought. No change in anxiety symptoms or threat interpretation was found between manipulation conditions. No evidence for the proposed combinational influence of speed and variability was found. Implications and avenues for therapeutic intervention are discussed.

The brain-sex theory of occupational choice: a counterexample

The brain-sex theory of occupational choice suggests that males and females in male-typical careers show a male pattern of cognitive ability in terms of better spatial than verbal performance on cognitive tests with the reverse pattern for females and males in female-typical careers, These differences are thought to result from patterns of cerebral functional lateralisation. This study Sought Such occupationally related effects using synonym generation (verbal ability) and mental rotation (spatial ability) tasks used previously. It also used entrants to these careers as participants to examine whether patterns of cognitive abilities might predate explicit training and practice. Using a population of entrants to sex-differentiated University Courses, a moderate occupational effect on the synonym generation task was found, along with a weak (p<.10) sex effect on the mental rotation task. Highest performance on the mental rotation task was by female Students in fashion design, a female-dominated occupation which makes substantial visuospatial demands and attracts many students with literacy problems such as dyslexia. This group then appears to be a counterexample to the brain-sex theory. However, methodological issues Surrounding previous Studies are highlighted: the simple synonym task appears to show limited discrimination of the sexes, leading to questions concerning the legitimacy of inferences about lateralisation based on scores from that test. Moreover, the human figure-based mental rotation task appears to tap the wrong aspect of visuospatial skill, likely to be needed for male-typical courses such as engineering, Since the fashion-clesign career is also one that attracts disproportionately many male students whose sexual orientation is homosexual, data were examined for evidence of female-typical patterns of cognitive performance among that subgroup. This was not found. This study therefore provides Do evidence for the claim that female-pattern cerebral functional lateralisation is likely in gay males.

Higher-order moments in the theory of diversifying and portfolio composition

This paper examines the role of higher-order moments in portfolio choice within an expected-utility framework. We consider two-, three-, four- and five-parameter density functions for portfolio returns and derive exact conditions under which investors would all be optimally plungers rather than diversifiers. Through comparative statics we show the importance of higher-order risk preference properties, such as riskiness, prudence and temperance, in determining plunging behaviour. Empirical estimates for the S&P500 provide evidence for the optimality of diversification.

Market impact of international sporting and cultural events

We study market reaction to the announcements of the selected country hosting the Summer and Winter Olympic Games, the World Football Cup, the European Football Cup and World and Specialized Exhibitions. We generalize previous results analyzing a large number and different types of mega-events, evaluate the effects for winning and losing countries, investigate the determinants of the observed market reaction and control for the ex ante probability of a country being a successful bidder. Average abnormal returns measured at the announcement date and around the event are not significantly different from zero. Further, we find no evidence supporting that industries, that a priori were more likely to extract direct benefits from the event, observe positive significant effects. Yet, when we control for anticipation, the stock price reactions around the announcements are significant.

Understanding the internet banking adoption by Portuguese customers - a unified theory of acceptance and use of technology and perceived risk application.

Trabalho de Projeto apresentado como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Impact of international consensus guidelines on antiviral therapy of chronic hepatitis C patients in Switzerland.

To assess the impact of international consensus conference guidelines on the attitude of Swiss specialists when facing the decision to treat chronic hepatitis C patients. Questionnaires focusing on the personal situation and treatment decisions were mailed to 165 patients who were newly diagnosed with hepatitis C virus (HCV) infection and enrolled into the Swiss Hepatitis C Cohort Study during the years 2002-2004. Survey respondents (n = 86, 52.1%) were comparable to non-respondents with respect to severity of liver disease, history of substance abuse and psychiatric co-morbidities. Seventy percent of survey respondents reported having been offered antiviral treatment. Patients deferred from treatment had less advanced liver fibrosis, were more frequently infected with HCV genotypes 1 or 4 and presented more often with a history of depression. There were no differences regarding age, socio-economic background, alcohol abuse, intravenous drug abuse or methadone treatment when compared with patients to whom treatment was proposed. Ninety percent of eligible patients agreed to undergo treatment. Overall, 54.6% of respondents and 78.3% of those considered eligible had actually received antiviral therapy by 2007. Ninety-five percent of patients reported high satisfaction with their own hepatitis C management. Consistent with latest international consensus guidelines, patients enrolled in the Swiss Hepatitis C Cohort with a history of substance abuse were not withheld antiviral treatment. A multidisciplinary approach is warranted to provide antiviral treatment to patients suffering from depression.