The functional singular value decomposition for bivariate stochastic processes

TL;DR

This paper explores the functional singular value decomposition (FSVD) as a versatile tool for analyzing bivariate stochastic processes, enabling decomposition, outlier detection, and mean estimation with competitive performance.

Contribution

It introduces the application of FSVD to decompose and analyze bivariate stochastic processes, demonstrating its utility in visualization, outlier detection, and mean estimation.

Findings

FSVD effectively decomposes bivariate stochastic processes.

FSVD estimators perform competitively with tensor-product splines.

FSVD aids in outlier detection and mean estimation.

Abstract

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.