Les applications les plus courantes des méthodes non paramétriques concernent l'estimation d'une fonction de régression (i.e. de l'espérance conditionnelle). Cependant, il est souvent intéressant de modéliser les quantiles conditionnels, en particulier lorsque la moyenne conditionnelle ne permet pas de représenter convenablement l'impact des covariables sur la variable dépendante. De plus, ils permettent d'obtenir des graphiques plus compréhensibles de la distribution conditionnelle de la variable dépendante que ceux obtenus avec la moyenne conditionnelle. A l'origine, la "quantification" était utilisée en ingénierie du signal et de l'information. Elle permet de discrétiser un signal continu en un nombre fini de quantifieurs. En mathématique, le problème de la quantification optimale consiste à trouver la meilleure approximation d'une distribution continue d'une variable aléatoire par une loi discrète avec un nombre fixé de quantifieurs. Initialement utilisée pour des signaux univariés, la méthode a été étendue au cadre multivarié et est devenue un outil pour résoudre certains problèmes en probabilités numériques.Le but de cette thèse est d'appliquer la quantification optimale en norme Lp à l'estimation des quantiles conditionnels. Différents cas sont abordés :covariable uni- ou multidimensionnelle, variable dépendante uni- ou multivariée. La convergence des estimateurs proposés est étudiée d'un point de vue théorique. Ces estimateurs ont été implémentés et un package R, nommé QuantifQuantile, a été développé. Leur comportement numérique est évalué sur des simulations et des données réelles. / One of the most common applications of nonparametric techniques has been the estimation of a regression function (i.e. a conditional mean). However it is often of interest to model conditional quantiles, particularly when it is felt that the conditional mean is not representative of the impact of the covariates on the dependent variable. Moreover, the quantile regression function provides a much more comprehensive picture of the conditional distribution of a dependent variable than the conditional mean function. Originally, the "quantization'" was used in signal and information theories since the fifties. Quantization was devoted to the discretization of a continuous signal by a finite number of "quantizers". In mathematics, the problem of optimal quantization is to find the best approximation of thecontinuous distribution of a random variable by a discrete law with a fixed number of charged points. Firstly used for a one-dimensional signal, themethod has then been developed in the multi-dimensional case and extensively used as a tool to solve problems arising in numerical probability.The goal of this thesis is to study how to apply optimal quantization in Lp-norm to conditional quantile estimation. Various cases are studied: one-dimensional or multidimensional covariate, univariate or multivariate dependent variable. The convergence of the proposed estimators is studied from a theoretical point of view. The proposed estimators were implemented and a R package, called QuantifQuantile, was developed. Numerical behavior of the estimators is evaluated through simulation studies and real data applications. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

With advances in high-throughput techniques, the availability of large-scale omics data has revolutionized the fields of medicine and biology, and has offered a better understanding of the underlying biological mechanisms. However, the high-dimensionality and the unknown association structure between different data types make statistical integration analyses challenging. In this dissertation, we develop three dimensionality reduction methods to detect nonlinear association structure using omics data. First, we propose a method for variable selection in a nonparametric additive quantile regression framework. We enforce a network regularization to incorporate information encoded by known networks. To account for nonlinear associations, we approximate the additive functional effect of each predictor with the expansion of a B-spline basis. We implement the group Lasso penalty to achieve sparsity. We define the network-constrained penalty by regulating the difference between the effect functions of any two linked genes (predictors) in the network. Simulation studies show that our proposed method performs well in identifying truly associated genes with fewer falsely associated genes than alternative approaches. Second, we develop a canonical correlation analysis (CCA)-based method, canonical distance correlation analysis (CDCA), and leverage the distance correlation to capture the overall association between two sets of variables. The CDCA allows untangling linear and nonlinear dependence structures. Third, we develop the sparse CDCA (sCDCA) method to achieve sparsity and improve result interpretability by adding penalties on the loadings from the CDCA. The sCDCA method can be applied to data with large dimensionality and small sample size. We develop iterative majorization-minimization-based coordinate descent algorithms to compute the loadings in the CDCA and sCDCA methods. Simulation studies show that the proposed CDCA and sCDCA approaches have better performance than classical CCA and sparse CCA (sCCA) in nonlinear settings and have similar performance in linear association settings. We apply the proposed methods to the Framingham Heart Study (FHS) to identify body mass index associated genes, the association structure between metabolic disorders and metabolite profiles, and a subset of metabolites and their associated type 2 diabetes (T2D)-related genes. / 2023-11-05T00:00:00Z

The U.S.-American foreclosure crisis and related economic crises have had severe and wide-reaching effects for the global economy, homeowners, and municipalities alike. These negative changes led to federal, state, regional, and local responses intended to prevent and mitigate foreclosures. As of yet, no research has examined the community- and neighborhood-level impacts of local foreclosure responses. This research seeks to determine the economic, physical, social, and political changes that resulted from these responses. A mixed methods case study of Cuyahoga County, Ohio, home to Cleveland, was used to identify local level foreclosure responses—i.e. those carried out at the county level and below—and their effects. The qualitative component was comprised of semi-structured stakeholder interviews, including local governmental representatives, advocacy groups, and neighborhood representatives. Two community subcases were investigated in depth to further examine the mechanisms and effects of foreclosure responses. The quantitative component supplements the qualitative component by means of a quantile regression model that examines relationships between foreclosure responses and changes in property value at the Census tract level, used to approximate communities. The model integrates data for the entire county and estimates coefficients at various quantiles of the dependent variable, which uncovers variations in the associations between the variables along the dependent variable’s distribution. That is, with quantile regression it is possible to determine whether foreclosure responses have different effects depending on community conditions. The results indicate that the national and local context are of particular importance when responding to the foreclosure crisis. Lackluster national level responses necessitated creative and innovative responses at the local level. The Cleveland region is characterized a weak housing market and its concomitant vacancy and abandonment problems. Thus, post-foreclosure responses that deal with blighted property are essential. A wide variety of foreclosure responses took place in Cuyahoga County, in the form of systems reform, foreclosure prevention, targeting, property acquisition and control, legal efforts, and community- and neighborhood-level efforts. Several strategies used in these responses emerged as themes: targeting, addressing blight, strengthening the social fabric, planning for the future, building institutions and organizational capacity, and advocacy. Physical and economic impacts are closely linked and are brought about especially by responses using targeting and blight reduction strategies. Social impacts, such as increased identification with, investment in, and commitment to the community occurred as the result of responses that used the strategies of strengthening the social fabric and planning a shared future for the community. Finally, the strategies of building institutions and organizational capacity and advocacy resulted in increased political power in the form of more local control and additional resources for neighborhoods and communities. These results provide deeper insight into the effects of the foreclosure crisis and local responses to it on neighborhoods and communities. This case study identifies the importance of targeting, blight removal, strengthening social bonds, planning for a shared future, increasing organizational capacity, and advocacy in addressing the foreclosure crisis on the community and neighborhood levels, especially in weak housing market cities where need far outstrips the available resources.

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Maximum size-density relationships (MSDR) are used to quantify differences across sites in the number of trees of a given size and species that can be supported per hectare. These relationships are important to managers who are trying to maximize basal area and wood volume. In my study, I examined MSDR across Alabama, Georgia, Louisiana, and Mississippi using US Forest Service, Forest Inventory and Analysis (FIA) data. I determined the impact of species-specific, specific gravity, functional traits, and environmental factors on MSDR using a quantile regression approach. Overall, I found that climatic factors had the greatest influence on MSDR, and that species shade and drought tolerance were more influential than specific gravity across the southeastern US.

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Habitat loss is the leading cause of species extinction. Protecting and managing habitat quality is vital to an organism's persistence, and essential to endangered species recovery. We conducted an investigation of habitat quality and potential impacts from climate change to piping plovers (Charadrius melodius) breeding on the barrier island ecosystem of New York, during 2003-2005. Our first step in this analysis was to examined the relationship between two common measures of habitat quality: density and productivity (Chapter 1). We used both central and limiting tendency data analysis to find that density significantly limited productivity across many spatial scales, especially broader scales. Our analysis of plover habitat quality (Chapter 2) focused on 1) identifying the spatial scaling of plovers to their environment; 2) determining the relative importance of four aspects of the environment (land cover, predation, management, and disturbance); and 3) determining the key environmental variables that influence productivity. We found that plover habitat selection occurred within a narrow range of spatial scales that was unique to each environmental variable. Further, we found that management and predation variables influenced population-level productivity relatively more than land cover and disturbance. Environmental variables with a significant positive influence on habitat quality were land management units, plover conservation educational signs, and symbolic string fencing erected around plover nesting areas. We found a significant negative relationship among density of people on ocean beaches, herring gull density, and land cover degradation. To quantify possible impact to plover habitat from future climate change (Chapter 3), we examined the extent of habitat change resulting from different estimates of sea-level rise (SLR) and storminess over the next 100 years. We found that the particular SLR estimate, habitat response, and storm type used to model climate changes influenced the amount of potential habitat available. Importantly, we observed synergy between SLR and storms resulting in the increasing impact of SLR and storms on plover habitat over the next 100 years. Finally, we found that coastal development contributed considerably to habitat loss when combined with climate changes. Our findings raise concerns regarding current plover recovery goals and management strategies. Density-dependent productivity may threaten the goal of a joint increase in both plover population and productivity. We advocate density monitoring and allocation of alternative nesting areas to provide the relief of possible high-density limitations. Based on our analysis of habitat selection and climate change threats, we call for a shift in management focus away from known breeding areas, towards ecosystem processes. Long-term conservation of piping plover habitat quality is more likely through protecting and promoting natural barrier island dynamics (i.e. overwash and migration) and minimizing human development on the barrier islands of New York State.

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