Threshold detection under a nonparametric regression model

"Threshold detection under a nonparametric regression model", organizado por CITMAga. Será impartido por Graciela Boente (Universidad de Buenos Aires e CONICET, Arxentina)

Data: Xoves 16 de novembro de 2023

Hora: ​​​13:00 h.

Duración: 1 hora

Lugar: Aula-Seminario 3 - Facultade de Ciencias Económicas e Empresariais da UVigo (Campus Universitario As Lagoas-Marcosende, Vigo)

Abstract:

Linear regression models have been extensively considered in the literature. However, in some practical applications they may not be appropriate all over the range of the covariate. In this paper, a more flexible model is introduced by considering a regression model Y = r(X) + ε where the regression function r(·) is assumed to be linear for large values in the domain of the predictor variable X. More precisely, we assume that r(x) = α0 + β0x for x > τ0, where the value τ0 is identified as the smallest value satisfying such a property. A penalized procedure is introduced to estimate the threshold τ0. The considered proposal focuses on a semiparametric approach since no parametric model is assumed for the regression function for values smaller than τ0. Consistency properties of both the threshold estimator and the estimators of (α0, β0) are derived, under mild assumptions. Through a numerical study, the small sample properties of the proposed procedure and the importance of introducing a penalization are investigated. The analysis of a real data set allows us to demonstrate the usefulness of the penalized estimators.
This is joint work with Florencia Leonardi, Daniela Rodriguez and Mariela Sued.