A1366
Title: Generalized distance covariance for linearity and independence in functional regression with missing at random responses
Authors: Pedro Galeano - Universidad Carlos III de Madrid (Spain) [presenting]
Manuel Febrero-Bande - University of Santiago de Compostela (Spain)
Wenceslao Gonzalez-Manteiga - University of Santiago de Compostela (Spain)
Abstract: A testing procedure is proposed to jointly assess the linearity between a scalar response and a functional covariate, and the independence between the covariate and the error term, in scalar-on-function regression models with responses missing at random (MAR). The test statistic corresponds to the generalized distance covariance between the functional covariate and the residuals obtained from a linear model fit. To address MAR responses, two slope estimation approaches based on functional principal components (FPCs) are considered: the simplified method, which excludes observations with missing responses, potentially leading to information loss; and (ii) the imputed method, which incorporates additional data by imputing missing responses using the simplified slope estimate. Cross-validation is employed to determine the optimal number of FPCs for each method. The distribution of the test statistic under the null hypothesis is calibrated using residual bootstrap. Monte Carlo simulations show that the proposed procedure can be quite powerful with appropriate choices of the semimetric and its associated parameters for the generalized distance covariance. Additionally, using the imputation method for estimation slightly increases the power of the procedure. The proposed methodology is illustrated through an application involving the modeling of average daily temperatures based on the average number of sunny days recorded at Spanish meteorological stations.
