An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on having the expected Fisher Information under normality based on the sample variance. The test statistic is then constructed as a ratio of the resulting likelihood against that of normality. Since the asymptotic distribution of this test statistic is not available, the critical values for n = 3 to 200 have been obtained by simulation and smoothed using polynomials. An extensive power study shows that the test has superior power against distributions that are symmetric and leptokurtic (long-tailed). Another advantage of the test over existing ones is the direct depiction of any deviation from normality in the form of a density estimate. This is evident when the test is applied to several real data sets. Testing of normality in residuals is also investigated. Various approaches in dealing with residuals being possibly heteroscedastic and correlated suffer from a loss of power. The approach with the fewest undesirable features is to use the Ordinary Least Squares (OLS) residuals in place of independent observations. From simulations, it is shown that one has to be careful about the levels of the normality tests and also in generalizing the results. / Ph. D.

Recent emphasis has been placed on merging regional forest inventory data with satellite-based information both to improve the efficiency of estimates of population totals, and to produce regional maps of forest variables. There are numerous ways in which forest class and structure variables may be modeled as functions of remotely sensed variables, yet surprisingly little work has been directed at surveying modem statistical techniques to determine which tools are best suited to the tasks given multiple objectives and logistical constraints. Here, a series of analyses to compare nonlinear and nonparametric modeling techniques for mapping a variety of forest variables, and for stratification of field plots, was conducted using data in the Interior Western United States. The analyses compared four statistical modeling techniques for predicting two discrete and four continuous forest inventory variables. The modeling techniques include generalized additive models (GAMs), classification and regression trees (CARTs), multivariate adaptive regression splines (MARS), and artificial neural networks (ANNs). Alternative stratification schemes were also compared for estimating population totals. The analyses were conducted within six ecologically different regions using a variety of satellite-based predictor variables. The work resulted in the development of an objective modeling box that automatically models spatial response variables as functions of any assortment of predictor variables through the four nonlinear or nonparametric modeling techniques. In comparing the different modeling techniques, all proved themselves workable in an automated environment, though ANNs were more problematic. When their potential mapping ability was explored through a simple simulation, tremendous advantages were seen in use of MARS and ANN for prediction over GAMs, CART, and a simple linear model. However, much smaller differences were seen when using real data. In some instances, a simple linear approach worked virtually as well as the more complex models, while small gains were seen using more complex models in other instances. In real data runs, MARS performed (marginally) best most often for binary variables, while GAMs performed (marginally) best most often for continuous variables. After considering a subjective "ease of use" measure, computing time and other predictive performance measures, it was determined that MARS had many advantages over other modeling techniques. In addition, stratification tests illustrated cost-effective means to improve precision of estimates of forest population totals. Finally, the general effect of map accuracy on the relative precision of estimates of population totals obtained under simple random sampling compared to that obtained under stratified random sampling was established and graphically illustrated as a tool for management decisions.

Survival Analysis in the context of Political Science is frequently used to study the duration of agreements, political party influence, wars, senator term lengths, etc. This paper surveys a collection of methods implemented on a modified version of the Power-Sharing Event Dataset (which documents civil war peace agreement durations in the Post-Cold War era) in order to identify the research questions that are optimally addressed by each method. A primary comparison will be made between a Cox Proportional Hazards Model using some advanced capabilities in the glmnet package, a Survival Random Forest Model, and a Survival SVM. En route to this comparison, issues including Cox Model variable selection using the LASSO, identification of clusters using Hierarchal Clustering, and discretizing the response for Classification Analysis will be discussed. The results of the analysis will be used to justify the need and accessibility of the Survival Random Forest algorithm as an additional tool for survival analysis.

Dans cette thèse, nous nous intéressons au problème de la prévision spatiale en considérant des modèles non paramétriques conditionnels dont la variable explicative est fonctionnelle. Plus précisément, les points étudiés pour décrire la co-variation spatiale entre une variable réponse réelle et une variable fonctionnelle sont le mode conditionnel et les quantiles conditionnels.En ce qui concerne le mode conditionnel, nous établissons la convergence presque complète, la convergence en norme Lp et la normalité asymptotique d'un estimateur à noyau. Ces propriétés asymptotiques sont obtenues sous des conditions assez générales telles, l'hypothèse de mélange forte et l'hypothèse de concentration de la mesure de probabilité de la variable explicative fonctionnelle. L'implémentation de l'estimateur construit en pratique est illustrée par une application sur des données météorologiques.Le modèle des quantiles conditionnels est abordé dans la deuxième partie de la thèse. Il est traité comme fonction inverse de la fonction de répartition conditionnelle qui est estimée par un estimateur à double noyaux. Sous les mêmes conditions que celles du modèle précédent, nous donnons l'expression de la vitesse de convergence en norme Lp et nous démontrons la normalité asymptotique de l'estimateur construit.Notre étude généralise au cas spatial de nombreux résultats déjà existant en série chronologique fonctionnelle. De plus, l'estimation de nos modèles repose sur une estimation préalable de la densité et de la fonction de répartition conditionnelles et permet de construire des régions prédictives, montrant ainsi l'apport de ce genre de modèles par rapport à la régression classique. / The main purpose of this thesis concerns the problem of spatial prediction using some nonparametric conditional models where the covariate variable is a functional one. More precisely, we treat the nonparametric estimation of the conditional mode and that of the conditional quantiles as spatial prediction tools alternative to the classical spatial regression of real response variable given a functional variable.Concerning the first model, that is the conditional mode, it is estimated by maximizing the spatial version of the kernel estimate of the conditional density. Under a general mixing condition and the concentration properties of the probability measure of the functional variable, we establish the almost complete convergence (with rate), the Lp consistency (with rate) and the asymptotic normality of the considered estimator. The usefulness of this estimation is illustrated by an application on real meteorological data.The model of the conditional quantiles is considered in the second part of this thesis and is treated as the inverse function of the conditional cumulative distribution function which is estimated by a double kernel estimator. Under the same general conditions as in the first model, we give the convergence rate in the Lp- norm and we show the asymptotic normality of the constructed estimator. These asymptotic results are closely related to the concentration properties on small balls of the probability measure of the underlying explanatory variable and the regularity of the conditional cumulative distribution function.Our study generalizes to spatial case some existing results in functional times series case. Finally, we highlight what our models brings compared to classical regression, discussing the use of our results as preliminary works to construct predictive regions.

Indiana University-Purdue University Indianapolis (IUPUI) / It is generally of interest to explore if the risk of death would be modified by medical conditions (e.g., illness) that have occurred prior. This situation gives rise to semicompeting risks data, which are a mixture of competing risks and progressive state data. This type of data occurs when a non-terminal event can be censored by a well-defined terminal event, but not vice versa. In the first part of this dissertation, the shared gamma-frailty conditional Markov model (GFCMM) is adopted because it bridges the copula models and illness-death models. Maximum likelihood estimation methodology has been proposed in the literature. However, we found through numerical experiments that the unrestricted model sometimes yields nonparametric biased estimation. Hence a practical guideline is provided for using the GFCMM that includes (i) a score test to assess whether the restricted model, which does not exhibit estimation problems, is reasonable under a proportional hazards assumption, and (ii) a graphical illustration to evaluate whether the unrestricted model yields nonparametric estimation with substantial bias for cases where the test provides a statistical significant result against the restricted model. However, the scientific question of interest that whether the status of non-terminal event alters the risk to terminal event can only be partially addressed based on the aforementioned approach. Therefore in the second part of this dissertation, we adopt a Markov illness-death model, whose transition intensities are essentially equivalent to the marginal hazards defined in GFCMM, but with different interpretations; we develop three nonparametric tests, including a linear test, a Kolmogorov-Smirnov-type test, and a L2-distance-type test, to directly compare the two transition intensities under consideration. The asymptotic properties of the proposed test statistics are established using empirical process theory. The performance of these tests in nite samples is numerically evaluated through extensive simulation studies. All three tests provide similar power levels with non-crossing curves of cumulative transition intensities, while the linear test is suboptimal when the curves cross. Eventually, the proposed tests successfully address the scientific question of interest. This research is applied to Indianapolis-Ibadan Dementia Project (IIDP) to explore whether dementia occurrence changes mortality risk. / 2022-05-06

京都大学 / 0048 / 新制・課程博士 / 博士(経済学) / 甲第19459号 / 経博第528号 / 新制||経||276(附属図書館) / 32495 / 京都大学大学院経済学研究科経済学専攻 / (主査)教授 西山 慶彦, 准教授 奥井 亮, 准教授 高野 久紀 / 学位規則第4条第1項該当 / Doctor of Economics / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(経済学) / 甲第20868号 / 経博第563号 / 新制||経||283(附属図書館) / 京都大学大学院経済学研究科経済学専攻 / (主査)教授 西山 慶彦, 准教授 山田 憲, 准教授 高野 久紀 / 学位規則第4条第1項該当 / Doctor of Economics / Kyoto University / DGAM

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