The master thesis deals with the joint EEG-fMRI analysis based on a heuristic model that describes the relationship between changes in blood flow in active brain areas and in the electrical activity of neurons. This work also discusses various methods of extracting of useful information from the EEG and their influence on the final result of joined analysis. There were tested averaging methods of electrodes interest, decomposition by principal components analysis and decomposition by independent component analysis. Methods of averaging and decomposition by PCA give similar results, but information about a stimulus vector can not be extracted. Using ICA decomposition, we are able to obtain information relating to the certain stimulation, but there is the problem in the final interpretation and selection of the right components in a blind search for variability coupled with the experiment. It was found out that although components calculated from the time sequence EEG are independent for each to other, their spectrum shifts are correlated. This spectral dependence was eliminated by PCA / ICA decomposition from vectors of spectrum shifts. For this method, each component brings new information about brain activity. The results of the heuristic approach were compared with the results of the joined analysis based on the relative and absolute power approach from frequency bands of interest. And the similarity between activation maps was founded, especially for the heuristic model and the relative power from the gamma band (20-40Hz).

<p dir="ltr">The National Flood Insurance Program (NFIP), which is run by the U.S. Federal Emergency Management Agency (FEMA), is presently under huge debt to the U.S. treasury. The debt is primarily caused by low flood insurance take-up rate, low willingness to pay for flood insurance, and large payouts after major disasters. Addressing this insolvency problem requires the NFIP to understand (1) what drives the demand for flood insurance so that it can be increased, (2) how risk factors contribute towards large flood insurance payouts so that effective risk reduction policies can be planned, and (3) how to predict the future flood insurance payouts so that the NFIP can be financially prepared. This research has answered these three fundamental questions by developing empirical models based on historical data. To answer the first question, this research has developed a propensity score-based causal model that analyzed one of the key components that influences the demand for flood insurance – the availability of post-disaster government assistance. It was found that the availability of the federal payout in a county in a year increased the number of flood insurance policies by 5.2% and the total insured value of the policies by 4.6% in the following year. Next, this research has developed Mixed Effects Regression model that quantified the causal relationships between the annual flood insurance payout in a county and flood related risk factors such as flood exposure, infrastructure vulnerability, social vulnerability, community resilience, and the number of mobile homes in the county. Based on the derived causal estimates, it was predicted that climate change, which is expected to increase flood exposure in coastal counties, will increase the annual NFIP payout in New Orleans, Louisiana by $2.04 billion in the next 30 years. Lastly, to make the NFIP financially prepared for future payouts, this research has developed a predictive model that can predict the annual NFIP payout in a county with adequate predictive accuracy. The predictive model was used to predict the NFIP payout for 2021 and it was able to predict that with a 9.8% prediction error. The outcomes of this research create new knowledge to inform policy decisions and strategies aimed at fortifying the NFIP. This includes strategies such as flood protection infrastructure, tailored disaster assistance, and other interventions that can bolster flood insurance uptake while mitigating the risk of substantial payouts. Ultimately, this research contributes to sustaining the NFIP's ability to provide vital flood insurance coverage to millions of Americans.</p>

當線性模型中包含隨機效果項時，若將之視為固定效果或直接忽略，往往會造成嚴重的推測偏差，故應以混合線性模型為架構。若模式中只包含一個隨機效果項，則模式中有兩個變異數成份，若包含 個隨機效果項，則模式中有 個變異數成份。本論文主要在介紹至少兩個變異數成份時固定效果及隨機效果線性組合的最佳線性不偏推測量（BLUP），及其推測區間之推導與建立。然而BLUP實為變異數比率的函數，若變異數比率未知，而以最大概似法（Maximum Likelihood Method）或殘差最大概似法（Residual Maximum Likelihood Method）估計出變異數比率，再代入BLUP中，則得到的是經驗最佳線性不偏推測量（EBLUP）。至於推測區間則與EBLUP的均方誤有關，本論文先介紹如何求算其漸近不偏估計量，再介紹EBLUP之推測誤差除以 後，其自由度的估算方法，據以建構推測區間。 / When random effects are contained in the model, if they are treated as fixed effects or ignore, then it may result in serious prediction bias. Instead, mixed linear model is to be considered. If there is one source of random effects, then the model has two variance components, while it has variance components, if the model contains random effects. This study primarily presents the derivation of the best linear unbiased predictor (BLUP) of a linear combination of the fixed and random effects, and then the conduction of the prediction interval when the model contains at least two variance components. However, BLUP is a function of variance ratios. If the variance ratios are unknown, we can replace them by their maximum likelihood estimates or residual maximum likelihood estimates, then we can get empirical best linear unbiased predictor (EBLUP). Because prediction interval is relating to the mean squared error (MSE) of EBLUP, so the study first introduces how to get its approximate unbiased estimator, m_a , then introduces how to evaluate the degrees of freedom of the ratio of the prediction error for the EBLUP and m_a ^1/2 , in order to use both of them to establish the prediction interval.

本文主要是在探討三個變數所構成之三維列聯表中，兩兩有序類別變數間的關係，而衡量的標準，我們則採用「兩兩變數所構成之二維列聯表中，相鄰兩列與相鄰兩行所求計出的相對成敗比（local odds ratios）」。在三維列聯表的資料架構下，我們可分別就固定某一變數水準之下兩個有序變數彼此間的「條件關係」，以及三個有序類別變數彼此兩兩間的「部分關係」，建構其各自的三維關係模型，並進行參數估計。此外，我們也提供必要的電腦程式，並舉出實例，加以說明。 / In analyzing a three-way contingency table with three ordinal variables, we can use association models suggested in Goodman (1979) to study the association between each pair of ordinal variables. The association was measured in terms of the local odds ratios formed from adjacent rows and adjacent columns of the cross-classification. This article investigates in great details the conditional association models and the partial association models for three-way cross-classifications. In addition, issues on estimating the para-meters in these two kinds of association models are discussed, and computer programs are provided. Some of the applications are illustrated.

Systematické řízení tepelných a elektrických toků v plně elektrických automobilech se stává velmi důležitým, protože v těchto typech automobilů není k dispozici dostatek odpadního tepla pro vytápění kabiny. Aby v zimním období nedocházelo ke snížení dojezdu, je nutné použití technologií, které umožní snížení spotřeby energie nutné k vytápění kabiny (např. tepelné čerpadlo, zásobník tepla). Je také zapotřebí vytvořit řídicí algoritmy pro tato zařízení, aby byl zajištěn jejich optimální provoz. V letním období je nezbytné řídit tepelné toky v rámci elektromobilu tak, aby nedocházelo k nadměrnému vybíjení baterie kvůli chlazení kabiny a dalších částí. Tato práce řeší jak návrh řídicích algoritmů, tak i vývoj rozhodovacího algoritmu, který zajistí směřování tepelných toků.

In vielen Anwendungen ist es notwendig, die stochastische Schwankungen der maximalen Abweichungen der nichtparametrischen Schätzer von Quantil zu wissen, zB um die verschiedene parametrische Modelle zu überprüfen. Einheitliche Konfidenzbänder sind daher für nichtparametrische Quantil Schätzungen der Regressionsfunktionen gebaut. Die erste Methode basiert auf der starken Approximation der empirischen Verfahren und Extremwert-Theorie. Die starke gleichmäßige Konsistenz liegt auch unter allgemeinen Bedingungen etabliert. Die zweite Methode beruht auf der Bootstrap Resampling-Verfahren. Es ist bewiesen, dass die Bootstrap-Approximation eine wesentliche Verbesserung ergibt. Der Fall von mehrdimensionalen und diskrete Regressorvariablen wird mit Hilfe einer partiellen linearen Modell behandelt. Das Verfahren wird mithilfe der Arbeitsmarktanalysebeispiel erklärt. Hoch-dimensionale Zeitreihen, die nichtstationäre und eventuell periodische Verhalten zeigen, sind häufig in vielen Bereichen der Wissenschaft, zB Makroökonomie, Meteorologie, Medizin und Financial Engineering, getroffen. Der typische Modelierungsansatz ist die Modellierung von hochdimensionalen Zeitreihen in Zeit Ausbreitung der niedrig dimensionalen Zeitreihen und hoch-dimensionale zeitinvarianten Funktionen über dynamische Faktorenanalyse zu teilen. Wir schlagen ein zweistufiges Schätzverfahren. Im ersten Schritt entfernen wir den Langzeittrend der Zeitreihen durch Einbeziehung Zeitbasis von der Gruppe Lasso-Technik und wählen den Raumbasis mithilfe der funktionalen Hauptkomponentenanalyse aus. Wir zeigen die Eigenschaften dieser Schätzer unter den abhängigen Szenario. Im zweiten Schritt erhalten wir den trendbereinigten niedrig-dimensionalen stochastischen Prozess (stationär). / In many applications it is necessary to know the stochastic fluctuation of the maximal deviations of the nonparametric quantile estimates, e.g. for various parametric models check. Uniform confidence bands are therefore constructed for nonparametric quantile estimates of regression functions. The first method is based on the strong approximations of the empirical process and extreme value theory. The strong uniform consistency rate is also established under general conditions. The second method is based on the bootstrap resampling method. It is proved that the bootstrap approximation provides a substantial improvement. The case of multidimensional and discrete regressor variables is dealt with using a partial linear model. A labor market analysis is provided to illustrate the method. High dimensional time series which reveal nonstationary and possibly periodic behavior occur frequently in many fields of science, e.g. macroeconomics, meteorology, medicine and financial engineering. One of the common approach is to separate the modeling of high dimensional time series to time propagation of low dimensional time series and high dimensional time invariant functions via dynamic factor analysis. We propose a two-step estimation procedure. At the first step, we detrend the time series by incorporating time basis selected by the group Lasso-type technique and choose the space basis based on smoothed functional principal component analysis. We show properties of this estimator under the dependent scenario. At the second step, we obtain the detrended low dimensional stochastic process (stationary).

No description available.

Ce mémoire de thèse porte sur la statistique inférentielle des données spatiales et/ou fonctionnelles. En effet, nous nous sommes intéressés à l’estimation de paramètres inconnus de certains modèles à partir d’échantillons obtenus par un processus d’échantillonnage aléatoire ou non (stratifié), composés de variables indépendantes ou spatialement dépendantes.La spécificité des méthodes proposées réside dans le fait qu’elles tiennent compte de la nature de l’échantillon étudié (échantillon stratifié ou composé de données spatiales dépendantes).Tout d’abord, nous étudions des données à valeurs dans un espace de dimension infinie ou dites ”données fonctionnelles”. Dans un premier temps, nous étudions les modèles de choix binaires fonctionnels dans un contexte d’échantillonnage par stratification endogène (échantillonnage Cas-Témoin ou échantillonnage basé sur le choix). La spécificité de cette étude réside sur le fait que la méthode proposée prend en considération le schéma d’échantillonnage. Nous décrivons une fonction de vraisemblance conditionnelle sous l’échantillonnage considérée et une stratégie de réduction de dimension afin d’introduire une estimation du modèle par vraisemblance conditionnelle. Nous étudions les propriétés asymptotiques des estimateurs proposées ainsi que leurs applications à des données simulées et réelles. Nous nous sommes ensuite intéressés à un modèle linéaire fonctionnel spatial auto-régressif. La particularité du modèle réside dans la nature fonctionnelle de la variable explicative et la structure de la dépendance spatiale des variables de l’échantillon considéré. La procédure d’estimation que nous proposons consiste à réduire la dimension infinie de la variable explicative fonctionnelle et à maximiser une quasi-vraisemblance associée au modèle. Nous établissons la consistance, la normalité asymptotique et les performances numériques des estimateurs proposés.Dans la deuxième partie du mémoire, nous abordons des problèmes de régression et prédiction de variables dépendantes à valeurs réelles. Nous commençons par généraliser la méthode de k-plus proches voisins (k-nearest neighbors; k-NN) afin de prédire un processus spatial en des sites non-observés, en présence de co-variables spatiaux. La spécificité du prédicteur proposé est qu’il tient compte d’une hétérogénéité au niveau de la co-variable utilisée. Nous établissons la convergence presque complète avec vitesse du prédicteur et donnons des résultats numériques à l’aide de données simulées et environnementales.Nous généralisons ensuite le modèle probit partiellement linéaire pour données indépendantes à des données spatiales. Nous utilisons un processus spatial linéaire pour modéliser les perturbations du processus considéré, permettant ainsi plus de flexibilité et d’englober plusieurs types de dépendances spatiales. Nous proposons une approche d’estimation semi paramétrique basée sur une vraisemblance pondérée et la méthode des moments généralisées et en étudions les propriétés asymptotiques et performances numériques. Une étude sur la détection des facteurs de risque de cancer VADS (voies aéro-digestives supérieures)dans la région Nord de France à l’aide de modèles spatiaux à choix binaire termine notre contribution. / This thesis is about statistical inference for spatial and/or functional data. Indeed, weare interested in estimation of unknown parameters of some models from random or nonrandom(stratified) samples composed of independent or spatially dependent variables.The specificity of the proposed methods lies in the fact that they take into considerationthe considered sample nature (stratified or spatial sample).We begin by studying data valued in a space of infinite dimension or so-called ”functionaldata”. First, we study a functional binary choice model explored in a case-controlor choice-based sample design context. The specificity of this study is that the proposedmethod takes into account the sampling scheme. We describe a conditional likelihoodfunction under the sampling distribution and a reduction of dimension strategy to definea feasible conditional maximum likelihood estimator of the model. Asymptotic propertiesof the proposed estimates as well as their application to simulated and real data are given.Secondly, we explore a functional linear autoregressive spatial model whose particularityis on the functional nature of the explanatory variable and the structure of the spatialdependence. The estimation procedure consists of reducing the infinite dimension of thefunctional variable and maximizing a quasi-likelihood function. We establish the consistencyand asymptotic normality of the estimator. The usefulness of the methodology isillustrated via simulations and an application to some real data.In the second part of the thesis, we address some estimation and prediction problemsof real random spatial variables. We start by generalizing the k-nearest neighbors method,namely k-NN, to predict a spatial process at non-observed locations using some covariates.The specificity of the proposed k-NN predictor lies in the fact that it is flexible and allowsa number of heterogeneity in the covariate. We establish the almost complete convergencewith rates of the spatial predictor whose performance is ensured by an application oversimulated and environmental data. In addition, we generalize the partially linear probitmodel of independent data to the spatial case. We use a linear process for disturbancesallowing various spatial dependencies and propose a semiparametric estimation approachbased on weighted likelihood and generalized method of moments methods. We establishthe consistency and asymptotic distribution of the proposed estimators and investigate thefinite sample performance of the estimators on simulated data. We end by an applicationof spatial binary choice models to identify UADT (Upper aerodigestive tract) cancer riskfactors in the north region of France which displays the highest rates of such cancerincidence and mortality of the country.

La llegada de plantas exóticas fuera de su rango de distribución original y su posterior asentamiento en ecosistemas naturales no es una excepción en las Islas Baleares. En la actualidad tenemos 308 especies no nativas naturalizadas y subespontáneas que representan el 16% del total de la flora Balear. En esta tesis se ha evaluado el estado de la cuestión a nivel global y local. Se ha confeccionado el primer catálogo de flora introducida y se ha analizado cuales de ellas son más abundantes y peligrosas; así como también qué ecosistemas son más vulnerables a la introducción de éstas. También se ha profundizado en el conocimiento de dos de las especies exóticas más peligrosas en el litoral Balear: Carpobrotus edulis y C. affine acinaciformis. Se ha evaluado su influencia sobre la polinización, su tasa de crecimiento bajo diferentes escenarios ambientales, se ha confeccionado un modelo de crecimiento y se ha evaluado su impacto sobre la composición y estructura de las comunidades nativas. / L'arribada de plantes exòtiques fora del seu rang de distribució original i el seu posterior assentament a ecosistemes naturals no és una excepció a les Illes Balears. A l'actualitat tenim 308 espècies no natives naturalitzades i subespontànies que representen el 16% del total de la flora Balear. En aquesta tesi s'ha avaluat l'estat de la qüestió a nivell global i local. S'ha confeccionat el primer catàleg de flora introduïda i s'han analitzat quines d'elles són més abundants i perilloses; així com també quins ecosistemes són més vulnerables a la introducció d'aquestes. També s'ha profunditzat en el coneixement de dues de les espècies exòtiques més perilloses del litoral Balear: Carpobrotus edulis y C. affine acinaciformis. S'ha avaluat la seva influència damunt els vectors de pol·linització, la taxa de creixement a diferents escenaris ambiental, s'ha confeccionat un model de creixement, i s'ha avaluat el seu impacte damunt la composició i estructura de les comunitats natives. / The constant arrival of exotic plants into areas outside their original distribution range and further settlement in natural ecosystems is not an exception in the Spanish Balearic archipelago. At the moment we have 308 non native species (naturalized and casual), the 16% from the total Balearic flora. This thesis has evaluated the exotic plant problematic at global and local level. We have elaborated the first exotic plants list, its distribution and abundance, as well as its degree of impact on the more vulnerable environments. We went deeply into the knowledge of two very invasive plants along the coast of the Balearic islands: Carpobrotus edulis y C. affine acinaciformis. We have evaluated its influence over pollen transmission, its growth rate at different environmental conditions, we have too elaborated a non liner growth model and its impact on composition and structure in natural communities