Robust location estimation with missing data.

STATTI. F. ; SUED, M.; YOHAI, V. J.

Congreso; Reunión Anual de la Unión Matemáica Argentina,; 2015

In this paper we propose a new procedure to estimate a location parameter of a variable y whenthere are missing data. The location parameter is defined though a robust location functional, e.g.,the median, the trimmed mean or an M-location functional. To compensate the presence of missingdata it is assumed that a covariable vector x is observed and that y and x are related by means ofa semi-parametric regression model. We obtain a lower bound for the breakdown point (LBBDP) ofthis procedure and show that it is higher than the one of the estimator presented in Sued and Yohai(SY). While the LBBDP of the SY procedure is at most 29.3, independently of the missing fraction,the LBBDP of the modified may be close to 50% when the missing fraction is close to 0.