SFB 303 Discussion Paper No. A - 598

Author: Kneip, Alois, and Klaus J. Utikal
Title: Inference for density families using functional principal component analysis
Abstract: We consider t=1,...T samples of i.i.d. observations {Xt1,....,Xtnt} from unknown population densities {ft}. To characterize differences and similarities of {ft} we assume their expansions into the first L principal components.

From the given observations {Xti} we study inference on the components and on their required number L. A detailed asymptotic theory is presented.

The method is applied in the analysis of yearly cross sectional samples of British households. Interpretation of the estimated principal components, and their scores give new insights into the evolution and interplay of household income and age distributions 1968-1988. From estimating their required numbers L we draw conclusions on the dimensionality of mixture models for describing the densities.

Keywords: k-sample problem, nonparameteric density estimation, kernel smoothing, functional principal components, density prediction, FES-data, incomedensity evolution.
JEL-Classification-Number: C13, C14, C21
Creation-Date: June 1999
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