The Bahadur-Kiefer Representation ofLpRegression Estimators
研究了线性回归模型中Lp估计量的Bahadur-Kiefer表示，给出了p≥1时该估计量的精确渐近展开式，适用于统计理论研究者。
We consider the following linear regression model: where are independent and identically distributed random variables, Y i , is real, Z i has values in R m , U i , is independent of Z i , and θ 0 is an m -dimensional parameter to be estimated. The L p estimator of θ 0 is the value 6n such that Here, we will give the exact Bahadur-Kiefer representation of θn, for each p ≥ 1. Explicitly, we will see that, under regularity conditions, where and c is a positive constant, which depends on p and on the random variable X .