The Repeated Median Intercept Estimator: Influence Function and Asymptotic Normality
Peter Rousseeuw () and
Journal of Multivariate Analysis, 1995, vol. 52, issue 1, 45-72
Given the simple linear regression model Yi = [alpha] + [beta]Xi + ei for i = 1, ..., n, we consider the repeated median estimator of the intercept [alpha], defined as [alpha]n = medi medj,j [not equal to] i (XjYi - XiYj)/(Xj - Xi). We determine the influence function and prove asymptotic normality for [alpha]n when the carriers Xi and error terms ei are random. The resulting influence function is bounded, and is the same as if the intercept is estimated by the median of the residuals from a preliminary slope estimator. With bivariate gaussian data the efficiency becomes 2/[pi] [approximate] 63.7%. The asymptotic results are compared with sensitivity functions and finite-sample efficiencies.
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