The functional singular value decomposition for bivariate stochastic processes

• Published in: Computational statistics & data analysis Vol. 54; no. 1; pp. 163 - 172
• Main Author: GERVINI, Daniel
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier 2010
• Series: Computational Statistics & Data Analysis
• Subjects: Exact sciences and technology; General topics; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic processes; Discriminant analysis; Data analysis; Tensor product; Singular value; Decomposition method; Multivariate analysis; Stochastic process; Mean estimation; Spline approximation; Surface; Numerical approximation; Functional; Outlier; Statistical computation; Simulation; Singular value decomposition
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2009.07.024

In this article we present some statistical applications of the functional singular value decomposition (FSVD). This tool allows us to decompose the sample mean of a bivariate stochastic process into components that are functions of separate variables. These components are sometimes interpretable functions that summarize salient features of the data. The FSVD can be used to visually detect outliers, to estimate the mean of a stochastic process or to obtain individual smoothers of the sample surfaces. As estimators of the mean, we show by simulation that FSVD estimators are competitive with tensor-product splines in some situations.