Robust nonparametric estimation with missing data

BOENTE, GRACIELA; GONZALEZ-MANTEIGA, WENCESLAO; PEREZ-GONZALEZ, ANA

JOURNAL OF STATISTICAL PLANNING AND INFERENCE

Elsevier

Lugar: Amsterdam; Año: 2009 vol. 139 p. 571 - 592

0378-3758

In this paper, under a nonparametric regression model, we introduce two families of robust procedures to estimate the regression function when missing data occur in the response. The first proposal is based on a local $M-$functional applied to the conditional distribution function estimate adapted to the presence of missing data. The second proposal imputes the missing responses using the local $M-$smoother based on the observed sample and then estimates the regression function with the completed sample. We show that the robust procedures considered are consistent and asymptotically normally distributed. A robust procedure to select the smoothing parameter is also discussed.