Inference for density families using functional principal component analysis
成果类型：
Article
署名作者：
Kneip, A; Utikal, KJ
署名单位：
Johannes Gutenberg University of Mainz
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/016214501753168235
发表日期：
2001
页码：
519-532
关键词：
摘要：
We consider t = 1,..., T samples of lid observations {X-1t,...,X-ntt} 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.