The overall goal of this project is to continue the development and implementation of methodology for density estimation by Fourier series methods. Subgoals include the following: (1). OPTIMIZED SERIES ESTIMATORS: The usefulness of dose-response, survival and other curve estimators will be increased by trading accuracy in one region of the curve for increased resolution in another, more important region. (2). MULTIVARIATE HYBRIDS: Work by Professor David Scott regarding multivariate nonparametric density estimation will be incorporated with the Fourier series methodology for displaying bivariate slices of density estimates. (3). SEMIPARAMETRIC DECOMPOSITION: The effectiveness of a semi-parametric method which separates density mixture symmetric subcomponents, and circumvents subcomponent model specification, will be enhanced. The advantage of this approach is that it can be used with the procedure described below to both select and fit a model, after subcomponents have been separated. (4). Q-Q AND P-P PLOT ALTERNATIVES: The methodology described in A, B and C will be applied to increase the resolution of an extended Q-Q graphical procedure. The extended procedure make it possible to select from among any fractional power or log transformation in conjunction with any member of five model systems.
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