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Abstract:
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In this paper we propose a framework for regression models where the response is a scalar with certain dependence structure and regressors are functions. In particular we assume that the data consists of clusters that have dependence within each cluster but are independent with respect to each other. We use generalized estimating equations to estimate the underlying parameters and establish their joint asymptotic normality.This asymptotic distribution is used to test asymptotically the significance of the regressors on the response variable. We apply these results on a family gene sequencing data. Here, individuals between families are independent but may be dependent within a family,thus necessitating for a method with above properties. Our simulations indicate that under certain conditions, functional approach has higher power for the high dimensional sequencing data as compared some current popular approaches.
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