Kneip, Alois; Utikal, Klaus J. Inference for density families using functional principal component analysis. (With comments). (English) Zbl 1019.62060 J. Am. Stat. Assoc. 96, No. 454, 519-542 (2001). Summary: We consider \(t=1,\dots,T\) samples of iid observations \(\{X_{1t}, \dots, X_{n_tt}\}\) from unknown population densities \(\{f_t\}\). To characterize differences and similarities of \(\{f_t\}\), we assume their expansions into the first \(L\) principal components. From the given observations \(\{X_{it}\}\), we study inference on the components and on their required number \(L\). A detailed asymptotic theory is presented. Our method is applied in the analysis of yearly cross-sectional samples of British households. Interpretation of the estimated principal components and their scores provides new insights into the evolution and interplay of household income and age distributions from 1968-1988. From estimating their required numbers \(L\), we draw conclusions on the dimensionality of mixture models for describing the densities. Cited in 54 Documents MSC: 62H25 Factor analysis and principal components; correspondence analysis 62P20 Applications of statistics to economics 62G07 Density estimation Keywords:density evolution; density mixtures; family expenditure survey data; household head age; household income; \(k\)-sample problem; kernel smoothing; prediction Software:fda (R) PDFBibTeX XMLCite \textit{A. Kneip} and \textit{K. J. Utikal}, J. Am. Stat. Assoc. 96, No. 454, 519--542 (2001; Zbl 1019.62060) Full Text: DOI