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<p>In this thesis, we apply the Ordinary Least Squares (OLS) and the Generalized Least Squares (GLS) methods for the estimation of Autoregressive Conditional Duration (ACD) models, as opposed to the typical approach of using the Quasi Maximum Likelihood Estimation (QMLE).</p> <p>The advantages of OLS and GLS as the underlying methods of estimation lie in their theoretical ease and computational convenience. The latter property is crucial for high frequency trading, where a transaction decision needs to be made within a minute. We show that both OLS and GLS estimates are asymptotically consistent and normally distributed. The normal approximation does not seem to be satisfactory in small samples. We also apply Residual Bootstrap to construct the confidence intervals based on the OLS and GLS estimates. The properties of the proposed methods are illustrated with intensive numerical simulations as well as by a case study on the IBM transaction data.</p> / Master of Science (MSc)

自2003年起隨著台灣壽險業國外投資比率不斷提高，至2010年底國外投資比率已達34.47%，因此為了探討壽險業國外投資與績效並了解相關因素之影響，本研究檢視壽險公司之市占率和各險種保費收入比率與國外投資比率之間的關係，同時亦檢視美國政府十年期公債殖利率與投資報酬率之間是否具有正向關係。另一方面，探討已公開發行公司是否因需揭露財務報表而與未公開發行公司之間在國外投資比率和投資績效上有所差異。 本文以2004年至2008年台灣25家壽險公司的長期資料（longitudinal data），分析總合（pooled）、固定效果(fixed effects)和隨機效果（random effects）迴歸模型，並檢視模型之適合性檢定。另因反應變數之密度估計具長尾之特性，所以亦使用Koenker（2004）和Geraci and Bottai（2007）提出的長期資料分量迴歸（quantile regression for longitudinal data）分析作為探討。實證結果顯示，若壽險公司的市占率愈高，則其資產配置於國外的比重亦相對地提高，且壽險和年金險比率與國外投資比率之間呈現顯著地正相關；此外，公開發行公司的國外投資比率顯著高於未公開發行公司。在投資績效方面，美國政府十年期公債殖利率與投資報酬率之間為顯著的正相關。 長期資料分量迴歸分析實證結果顯示，當使用Koenker（2004）提出之方法時，則一般（ordinary）分量迴歸在50%、75%和90%條件分量下，隨著樣本期間年度的增加，壽險業的國外投資報酬率相對地上升；在10% 和25% 條件分量下，壽險公司市占率與國外投資報酬率之間是顯著的正相關。而使用Geraci and Bottai（2007）提出之隨機效果分量迴歸方法時，在50%條件分量下，國外投資比率與國外投資報酬率之間為顯著地正相關，再者匯率風險將降低台灣壽險業國外投資的意願，然而實行避險策略是有益於投資績效的提升。 / The foreign investment ratio for the life insurance industry in Taiwan has risen constantly since 2003 and reached 34.47% in 2010. In order to explore foreign investment and performance, and understand the impact of relevant factors in the life insurance industry, this study examines the relationship between the market shares of life insurance companies, types of premium income ratio and the foreign investment ratio. Simultaneously, this study also examines the relationship between the 10-year US Treasury Bond Yield Currency and investment return.On the other hand, we explore whether the difference between the publicly traded companies and non-publicly traded companies on the foreign investment ratio and the investment performance. In this dissertation, we analyze 25 Taiwanese life insurance companies between 2004 and 2008 using the pooled, fixed effects and random effects regression model. Due to the distribution of the response variable is characterized by the long tail, we explore the use of the quantile regression for longitudinal data by Koenker(2004)and Geraci and Bottai(2007). The empirical results show that the more market share of life insurance companies, the higher foreign investment ratio and there is significantly positive correlation between the life insurance, annuity ratio and the foreign investment ratio. In addition, the publicly traded company's foreign investment ratio is significantly higher than non-publicly traded company. In terms of investment performance, it’s significantly positive correlation between the U.S. 10-year Treasury Bond Yield Currency and return on investment. The empirical results about quantile regression for longitudinal data show that the return on foreign investment relatively enhance for the life insurance industry with the increase of the year during the sample period under the 50%,75% and 90% conditional qauntile when using the ordinary quantile regression proposed by Koenker(2004). There is significantly positive correlation between the market share and the return on foreign investment under the 10% and 25% conditional qauntile. When using the method proposed by Geraci and Bottai(2007), there is significantly positive correlation between the foreign investment ratio and the return on foreign investment under the 50% conditional qauntile. Furthermore, exchange rate risk will reduce the foreign investment willingness of the life insurance industry in Taiwan. However, the implementation of the hedging strategy is beneficial to enhance investment performance for the life insurance industry.

- 1 - Abstract The intent of this thesis is to evaluate the differences in facial morphology of children between 3 and 15 years of age based on 3D facial models and cross-sectional data. Due to improper use of cross-sectional data for studying growth, the next part of the thesis is focused on the comparison of cross-sectional and longitudinal approaches in research. The longitudinal observation of facial developmental changes can be considered as actual growth. The cross-sectional database contains 839 3D facial models (397 boys, 442 girls). Three previously published longitudinal databases were used for comparison. Their age intervals were as follows: 3 to 6 years (12 boys, 14 girls), 6 to 12 years (15 boys, 18 girls), 12 to 15 years (23 boys, 22 girls). Geometric morphometric methods were used to analyse facial models (Coherent Point Drift - Dense Correspondance Analysis, Per Vertex T-Test and Principal Component Analysis). The results were visualized using superimposition colour maps, shell distance significance maps and their interlacing. When annual consecutive age intervals were used for cross-sectional data, we could not observe the fluency of differences in facial morphology between age categories, which we can observe during actual growth. When wider age intervals were used for cross-sectional...

- 1 - Abstract The intent of this thesis is to evaluate the differences in facial morphology of children between 3 and 15 years of age based on 3D facial models and cross-sectional data. Due to improper use of cross-sectional data for studying growth, the next part of the thesis is focused on the comparison of cross-sectional and longitudinal approaches in research. The longitudinal observation of facial developmental changes can be considered as actual growth. The cross-sectional database contains 839 3D facial models (397 boys, 442 girls). Three previously published longitudinal databases were used for comparison. Their age intervals were as follows: 3 to 6 years (12 boys, 14 girls), 6 to 12 years (15 boys, 18 girls), 12 to 15 years (23 boys, 22 girls). Geometric morphometric methods were used to analyse facial models (Coherent Point Drift - Dense Correspondance Analysis, Per Vertex T-Test and Principal Component Analysis). The results were visualized using superimposition colour maps, shell distance significance maps and their interlacing. When annual consecutive age intervals were used for cross-sectional data, we could not observe the fluency of differences in facial morphology between age categories, which we can observe during actual growth. When wider age intervals were used for cross-sectional...

Spatial-temporal autologistic models are useful models for binary data that are measured repeatedly over time on a spatial lattice. They can account for effects of potential covariates and spatial-temporal statistical dependence among the data. However, the traditional parametrization of spatial-temporal autologistic model presents difficulties in interpreting model parameters across varying levels of statistical dependence, where its non-negative autocovariates could bias the realizations toward 1. In order to achieve interpretable parameters, a centered spatial-temporal autologistic regression model has been developed. Two efficient statistical inference approaches, expectation-maximization pseudo-likelihood approach (EMPL) and Monte Carlo expectation-maximization likelihood approach (MCEML), have been proposed. Also, Bayesian inference is considered and studied. Moreover, the performance and efficiency of these three inference approaches across various sizes of sampling lattices and numbers of sampling time points through both simulation study and a real data example have been studied. In addition, We consider the imputation of missing values is for spatial-temporal autologistic regression models. Most existing imputation methods are not admissible to impute spatial-temporal missing values, because they can disrupt the inherent structure of the data and lead to a serious bias during the inference or computing efficient issue. Two imputation methods, iteration-KNN imputation and maximum entropy imputation, are proposed, both of them are relatively simple and can yield reasonable results. In summary, the main contributions of this dissertation are the development of a spatial-temporal autologistic regression model with centered parameterization, and proposal of EMPL, MCEML, and Bayesian inference to obtain the estimations of model parameters. Also, iteration-KNN and maximum entropy imputation methods have been presented for spatial-temporal missing data, which generate reliable imputed values with the reasonable efficient imputation time.

Longitudinal data occur frequently in medical studies and covariates measured by error are typical features of such data. Generalized linear mixed models (GLMMs) are commonly used to analyse longitudinal data. It is typically assumed that the random effects covariance matrix is constant across the subject (and among subjects) in these models. In many situations, however, this correlation structure may differ among subjects and ignoring this heterogeneity can cause the biased estimates of model parameters. In this thesis, following Lee et al. (2012), we propose an approach to properly model the random effects covariance matrix based on covariates in the class of GLMMs where we also have covariates measured by error. The resulting parameters from this decomposition have a sensible interpretation and can easily be modelled without the concern of positive definiteness of the resulting estimator. The performance of the proposed approach is evaluated through simulation studies which show that the proposed method performs very well in terms biases and mean square errors as well as coverage rates. The proposed method is also analysed using a data from Manitoba Follow-up Study. / February 2017

Ordinal scales are commonly used to measure health status and disease related outcomes in hospital settings as well as in translational medical research. Notable examples include cancer staging, which is a five-category ordinal scale indicating tumor size, node involvement, and likelihood of metastasizing. Glasgow Coma Scale (GCS), which gives a reliable and objective assessment of conscious status of a patient, is an ordinal scaled measure. In addition, repeated measurements are common in clinical practice for tracking and monitoring the progression of complex diseases. Classical ordinal modeling methods based on the likelihood approach have contributed to the analysis of data in which the response categories are ordered and the number of covariates (p) is smaller than the sample size (n). With the emergence of genomic technologies being increasingly applied for obtaining a more accurate diagnosis and prognosis, a novel type of data, known as high-dimensional data where the number of covariates (p) is much larger than the number of samples (n), are generated. However, corresponding statistical methodologies as well as computational software are lacking for analyzing high-dimensional data with an ordinal or a longitudinal ordinal response. In this thesis, we develop a regularization algorithm to build a parsimonious model for predicting an ordinal response. In addition, we utilize the classical ordinal model with longitudinal measurements to incorporate the cutting-edge data mining tool for a comprehensive understanding of the causes of complex disease on both the molecular level and environmental level. Moreover, we develop the corresponding R package for general utilization. The algorithm was applied to several real datasets as well as to simulated data to demonstrate the efficiency in variable selection and precision in prediction and classification. The four real datasets are from: 1) the National Institute of Mental Health Schizophrenia Collaborative Study; 2) the San Diego Health Services Research Example; 3) A gene expression experiment to understand `Decreased Expression of Intelectin 1 in The Human Airway Epithelium of Smokers Compared to Nonsmokers' by Weill Cornell Medical College; and 4) the National Institute of General Medical Sciences Inflammation and the Host Response to Burn Injury Collaborative Study.

Em Lora e Singer (Statistics in Medicine, 2008), propusemos um modelo Beta- Binomial/Poisson p-variado para análise dos dados provenientes de um estudo que consistiu em contar o número de tentativas e acertos de um exercício manual com duração de um minuto realizado por doentes de Parkinson, antes e depois de um treinamento. O objetivo era verificar se o treinamento aumentava o número de tentativas e a porcentagem de acerto, o que destaca o aspecto bivariado do problema. Esse modelo leva tais características em consideração, usa uma distribuição adequada para dados de contagem e ainda acomoda a sobredispersão presente na contagem dos acertos. Como generalização, inicialmente, propomos um modelo Beta-Binomial/Poisson-Gama que acomoda sobredispersão também para as contagens dos totais de tentativas, além incluir covariâncias possivelmente diferentes entre as contagens em diversos instantes de avaliação. Neste novo modelo, introduzimos um parâmetro que relaciona o total de tentativas com a probabilidade de acerto, tornando-o ainda mais geral. Obtemos estimadores de máxima verossimilhança dos parâmetros utilizando um algoritmo de Newton-Raphson. Consideramos um outro conjunto de dados provenientes do mesmo estudo para ilustração da metodologia proposta. / In Lora and Singer (Statistics in Medicine, 2008), we proposed a Beta-Binomial/Poisson p-variate model to analyze data from a study which consists in counting the number of trials and successes of a manual exercise in one minute periods, done by Parkinsons disease patients, before and after a training. The purpose was to verify if the training improves the number of trials and the percentage of success, which emphasizes the bivariate aspect of the problem. This model considers these characteristics, uses an adequate distribution to count data and settles the overdispersion suggested in the number os successes. As a generalization, initially, we propose a Beta-Binomial/Poisson-Gama model which also settles the overdispersion suggested by the total number of trials, besides includes possible different covariances between total trial counts in different evaluation instants. In this new model, we introduce a parameter that links the total trials with the success probability, making it even more general. We obtain maximum likelihood estimators for the parameters using an Newton-Raphson algorithm. We consider another data from the same study to illustrate the proposal methodology.

Dans les pays en développement, l'imbrication des activités économiques au sein du ménage rend la mesure de la dynamique des revenus complexe, en particulier lorsque les périodes étudiées sont longues. Le contexte choisi est celui de la décennie 1995-2005 à Madagascar, une période particulièrement intéressante puisqu'il s'agit du premier épisode de croissance soutenue et quasi-ininterrompue depuis l'indépendance du pays en 1960. En utilisant des données collectées auprès de ménages ruraux et urbains et d'entreprises du secteur informel, en coupe et en panel, les trois chapitres étudient chacun un aspect particulier du problème de mesure la dynamique de la pauvreté sur longue période dans un contexte d'imbrication forte des unités productives et des ménages. Le premier chapitre examine la dynamique du secteur informel à Antananarivo en tenant compte de sa nature très hétérogène. Le deuxième mesure l'écart de performance entre les unités de production dirigées par des femmes et celles dirigées par des hommes. Il teste l’existence d’effets différenciés selon le genre des normes de partage et d’allocation des tâches au sein du ménage sur l’efficience technique des entreprises. Le troisième chapitre discute l’opportunité de suivre des migrants dans les enquêtes longitudinales. L’étude des micro-entreprises doit tenir compte de leur environnement familial et social, pour prendre la pleine mesure des contraintes qui pèsent sur elles. Des recherches sur le comportement et la rationalité économique des ménages urbains apparaissent nécessaire. En l'absence de données longitudinales, la principale limite du travail réside dans l'impossibilité de décrire la démographie des entreprises informelles dans le temps. Il semble indispensable d’imaginer des dispositifs de collectes de données innovants permettant de suivre ces unités de production dans le temps / In developing countries, the complex interdependence of households, individuals and businesses makes the measurement of welfare dynamics challenging, especially over a long period, because economic activities are predominantly embedded in households. The context we have chosen, Madagascar between 1995 and 2005, is particularly interesting because it corresponds to an unprecedented period of growth interrupted only by a recession in 2002 due to a political crisis. Using urban, rural, cross-sectional and panel data, the three essays presented attempt to shed light on various aspects of welfare dynamics over a long period in Madagascar, with a special focus on the imbrication of productive activities, households and individuals. The first essay studies informal sector dynamics in Antananarivo with a special attention on its heterogeneous nature. The second measures the extent of the gender performance gap among informal entrepreneurs and explores the existence of gender-differentiated effects of sharing norms and the allocation of tasks within the household on the technical efficiency of enterprises. Finally, the third essay is a methodological contribution on the relevance of tracking movers in panel data collection in rural areas. Studying microenterprises within their family and social environment is necessary to fully grasp the constraints on productive activities. More research is necessary on the behavior and economic rationality of urban households. The lack of panel data on informal businesses limits what can be said on their demography, especially over a long period. There is a pressing need for innovative data collection devices which follow these production units over time