The thesis deals with brief introduction of the quantile regression theory. The thesis is divided into three thematic parts. In the first part the thesis deals with general introduction to the quantile regression, with theoretical aspects regarding quantile regression and with basic approaches to estimation of quantile regression parameters. The second part of the thesis focuses on general and asymptotic properties of the quantile regression. Goal of this part is to compare the quantile regression with traditional OLS regression and outline its possible application. In the third part the thesis describes statistical inference, construction of the confidence intervals and testing statistical hypotheses about quantile regression parameters. The goal of this part is to introduce traditional approach and the approach based on resampling procedures and in the end of the day perform mutual comparison of different approaches eventually propose partial modification.

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

This thesis develops a methodology for the construction of generalized families of probability distributions in the quantile statistical universe, that is, distributions specified in terms of their quantile functions. The main benefit of the proposed methodology is that it generates quantile-based distributions with skewness-invariant measures of kurtosis. The skewness and kurtosis can therefore be identified and analyzed separately. The key contribution of this thesis is the development of a new type of the generalized lambda distribution (GLD), using the quantile function of the generalized Pareto distribution as the basic building block (in the literature each different type of the GLD is incorrectly referred to as a parameterization of the GLD – in this thesis the term type is used). The parameters of this new type can, contrary to existing types, easily be estimated with method of L-moments estimation, since closed-form expressions are available for the estimators as well as for their asymptotic standard errors. The parameter space and the shape properties of the new type are discussed in detail, including its characterization through L-moments. A simple estimation algorithm is presented and utilization of the new type in terms of data fitting and approximation of probability distributions is illustrated. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Statistics / unrestricted

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.

No description available.

No description available.

No description available.

No description available.

DNA methylation plays a key role in disease analysis, especially for studies that compare known large scale differences in CpG sites, such as cancer/normal studies or between-tissues studies. However, before any analysis can be done, data normalization and preprocessing of methylation data are required. A useful data preprocessing pipeline for large scale comparisons is Functional Normalization (FunNorm), (Fortin et al., 2014) implemented in the minfi package in R. In FunNorm, the univariate quantiles of the methylated and unmethylated signal values in the raw data are used to preprocess the data. However, although FunNorm has been shown to outperform other preprocessing and data normalization processes for these types of studies, it does not account for the correlation between the methylated and unmethylated signals into account; the focus of this paper is to improve upon FunNorm by taking this correlation into account. The concept of a bivariate quantile is used in this study as an attempt to take the correlation between the methylated and unmethylated signals into consideration. From the bivariate quantiles found, the partial least squares method is then used on these quantiles in this preprocessing. The raw datasets used for this research were collected from the European Molecular Biology Laboratory - European Bioinformatics Institute (EMBL-EBI) website. The results from this preprocessing algorithm were then compared and contrasted to the results from FunNorm. Drawbacks, limitations and future research are then discussed. / Thesis / Master of Science (MSc)

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.