Statistical Modelling and Dimension Reduction for Functional Data

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9803627Jane-Ling WangCurve or functional data are of increasing importance due to enhenced high performance computing facilities and increased awareness that such data require special methods of analysis. Such data arise for example in longitudinal studies and in aging research. This research involves the development of new nonparametric methods to analyze such data. The focus is on procedures which involve both multivariate techniques and smoothing methods. Of particular interest are ANOVA and regression models for curve data. Emphasis is given on methods viewing the curve data as generalizations of one or several stochastic processes. Given a Karhunen-Loeve representation of the underlying processes, ANOVA for curve data can be based on the estimated principal components or on the whole curve. In this context, curve registration is of interest. New regression methods for curve data is also proposed. One of the regression methods extends the karhunen-Loeve representation to allow covariates to act on either the mean function or the covariance functions of the representation. Another regression method extends the sliced inverse regression (SIR) method for multivariate data to curve data. Such an approach for curve data has the advantage of model flexibility and accomplishes the goal of dimension reduction before the nonparametric model fitting stage. It is computationally simple and suitable as an exploratory tool for functional data analysis.This research is motivated by collaborative research of the investigator on biological lifespan and aging. Recently, there is an accelerated interest in aging research partly due to its financial and policy impact and partly due to its intrinsic aspects. The elderly population (age 65 or above) will swell as the babyboomers begin turning 65 in the year 2011 so its impact is self-evident. The investigator has been active in this research area through the analysis of large data sets on the aging of mediterranean fruit flies (medflies). One of these data sets contains the complete reproduction history, in terms of the number of eggs laid daily, for each of the 1,000 female medflies in the experiment. The scientific question is how to relate reproductive traits to survival and mortality of the medflies. Another data set on the nutrition effects to mortality of male and female medflies is studied. Here the scientific question of interest is to relate nutrition and gender effects to aging. The procedures developed in this study are applied to these and other medfly data to judge the practicality and scientific merits of the methods. They also help to address the underlying biological issues about the aging process.