對稱型迴歸分位向量和它應用在非線性迴歸的穩健估計

Abstract

分佈的α分位向量在分辨離群值上，有如指標般的的非常有用。我們提出 對稱型分位向量 來估計未知的非線性迴歸分位向量。在做大樣本分析而 α值很大或很小時，我們發現對稱 型分位向量比Koenker和 Bassett提 出的迴歸分位向量有更小的近似變異數。所以在分辨 離群值時，對稱型 分位向量是比較有用的。在幾個誤差分配為重尾分配的例子中，我們採 用對稱型分位向量去製造加權平均數來估計非線型迴歸的參數β 。我們 發現這些估計量 的近似變異數可以 非常接近Cramer-Rao 下限。這是 一些常用的穩健和 非穩健估計量所不能達 到的。 Populational conditional quantiles in terms of percentage α are useful as i ndices foridentifying outliers. We propose a class of symmetric quantiles for estimating the unknownnonlinear regression conditional quantiles. In a large s ample analysis, the symmetric quantileis more efficient in the sense of smalle r asymptotic variances than the regression quantileof Koenker and Bassett(1978 ) for smaller large α's .Thus, it is useful playing the role for identifying outliers. In examples of estimating nonlinear regression parameters by weight ed means constructed by the symmetric quantiles, we show that their asymptoti c variances can be very close to the Cramer-Rao lower bound under heavy tail error distributions whereas the usual robust and nonrobust estimators are not .