Some Problems in Nonparametric Function Estimation

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The investigator continues the methodological/theoretical/algorithmic developments and the software implementation of smoothing spline ANOVA models. Through the inclusion/exclusion of selected terms in functional ANOVA structures, rich modeling options are made available in the settings of regression, density estimation, and hazard rate estimation; the popular additive models are special cases. Among specific tasks in this phase of the research are (i) the separate model configurations of variables of different natures such as geographic locations and time for seasonal effect, (ii) conditional density estimation on generic domains which induce regression models with all sorts of responses including multivariate ones with mixtures of discrete, continuous, and possibly other types, (iii) Fast computation for multivariate density estimation which makes nonparametric graphical models practically feasible, and (iv) hazard estimation with censored lifetime data and frailty terms. Also explored are the spectral analysis of non-stationary time series and spike trains.As nonparametric extensions of the widely used (generalized) linear models, the methods being developed provide empowering modeling tools for researchers in a broad spectrum of application areas to extract fine features from the ever larger data sets they collect; documented past applications were found in biomedical studies, epidemiology, natural resource management, etc. The end product of the proposed research is open-source software with a friendly user-interface in a popular platform with a diverse user base, which facilitates the routine use of the tools being developed by practitioners and thus enhances the infrastructure for information-processing.