ASYMPTOTIC THEORY FOR SOME HIGH BREAKDOWN POINT ESTIMATORS
研究了回归中高崩溃点估计量的渐近性质，特别是平滑最小中位数平方估计量，推导了其极限过程，适用于时间序列和异常值识别。
High breakdown point estimators in regression are robust against gross contamination in the regressors and also in the errors; the least median of squares (LMS) estimator has the additional property of packing the majority of the sample most tightly around the estimated regression hyperplane in terms of absolute deviations of the residuals and thus is helpful in identifying outliers. Asymptotics for a class of high breakdown point smoothed LMS estimators are derived here under a variety of conditions that allow for time series applications; joint limit processes for several smoothed estimators are examined. The limit process for the LMS estimator is represented via a generalized Gaussian process that defines the generalized derivative of the Wiener process.