文章基本信息

标题：Structured penalties for functional linear models—partially empirical eigenvectors for regression
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作者：Timothy W. Randolph ; Jaroslaw Harezlak ; Ziding Feng 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2012
卷号：6
页码：323-353
DOI：10.1214/12-EJS676
语种：English
出版社：Institute of Mathematical Statistics
摘要：One of the challenges with functional data is incorporating geometric structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear model is often used to estimate the relationship between the predictor functions and scalar responses. Common approaches to the problem of estimating a coefficient function typically involve two stages: regularization and estimation. Regularization is usually done via dimension reduction, projecting onto a predefined span of basis functions or a reduced set of eigenvectors (principal components). In contrast, we present a unified approach that directly incorporates geometric structure into the estimation process by exploiting the joint eigenproperties of the predictors and a linear penalty operator. In this sense, the components in the regression are ‘partially empirical’ and the framework is provided by the generalized singular value decomposition (GSVD). The form of the penalized estimation is not new, but the GSVD clarifies the process and informs the choice of penalty by making explicit the joint influence of the penalty and predictors on the bias, variance and performance of the estimated coefficient function. Laboratory spectroscopy data and simulations are used to illustrate the concepts.