On function-on-function regression: partial least squares approach


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Beyaztas U. , Shang H. L.

ENVIRONMENTAL AND ECOLOGICAL STATISTICS, vol.27, no.1, pp.95-114, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1007/s10651-019-00436-1
  • Title of Journal : ENVIRONMENTAL AND ECOLOGICAL STATISTICS
  • Page Numbers: pp.95-114
  • Keywords: Basis function, Functional data, NIPALS, Nonparametric smoothing, SIMPLS, VARYING-COEFFICIENT MODELS, PRINCIPAL COMPONENT REGRESSION, LINEAR-REGRESSION, SELECTION

Abstract

Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical procedures, including least squares, maximum likelihood, and maximum penalized likelihood, have been proposed to estimate such function-on-function regression models. However, these estimation techniques produce unstable estimates in the case of degenerate functional data or are computationally intensive. To overcome these issues, we proposed a partial least squares approach to estimate the model parameters in the function-on-function regression model. In the proposed method, the B-spline basis functions are utilized to convert discretely observed data into their functional forms. Generalized cross-validation is used to control the degrees of roughness. The finite-sample performance of the proposed method was evaluated using several Monte-Carlo simulations and an empirical data analysis. The results reveal that the proposed method competes favorably with existing estimation techniques and some other available function-on-function regression models, with significantly shorter computational time.