Robust location estimation with missing data

MARIELA SUED; VICTOR J. YOHAI

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE

WILEY-BLACKWELL PUBLISHING, INC

Lugar: Londres; Año: 2013 vol. 41 p. 111 - 132

0319-5724

In a missing data setting, we have a sample in which a vector of explanatory variables x_i is observed for every subject i, while scalar responses y_i are missing by happenstance on some individuals. In this work we propose robust estimators of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response’s distribution. In particular, strongly consistent estimators of any continuous location functional, such as the median, L-functionals and M-functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimators is also derived.