Generalized distance covariance for linearity and independence in scalar-on-function regression with missing at random responses

P. Galeano San Miguel

A testing procedure is introduced to jointly assess linearity and independence between the covariate and the error term in the scalar-on-function regression model with responses missing at random (MAR). The test statistic is defined as the generalized distance covariance between the functional covariate and the residuals from a fitted linear model. To handle MAR responses, three slope estimation approaches based on functional principal components (FPCs) are considered: $\left(i\right)$ the simplified method, which discards observations with missing responses at the cost of potential information loss; $\left(ii\right)$ the predicted value imputation method, which fills missing responses using a regression-based approach; and $\left(iii\right)$ the noise-augmented imputation method, which incorporates a random error term into the regression imputation to better preserve variability. In all cases, the optimal number of FPCs is selected via cross-validation. The null distribution of the test statistics is calibrated through wild bootstrap. Monte Carlo experiments indicate that the procedure achieves high power when the semimetric and its parameters associated with the generalized distance covariance are appropriately chosen, with statistics based on the predicted value imputation method yielding a modest power gain. Finally, the proposed methodology is illustrated with an application modeling average number of sunny days observed at Spanish meteorological stations as a function of the average daily temperatures.

Keywords: Functional linear model, Functional principal components, Generalized distance covariance, Goodness-of-fit tests, Missing at random, Wild bootstrap.

GT Análisis de Datos Funcionales I
September 4, 2026  9:00 AM
Aula 30

C. Díaz-Louzao, M. C. Aguilera-Morillo, A. J. Ferrer-Riquelme

S. Novo Díaz, G. Aneiros Pérez

D. Diz Castro, M. Febrero Bande, W. González Manteiga

A. Elías Fernández