邊界附近的偏態區域線性估計

Abstract

本文考慮 Choi and Hall (1998) 中，為降低區域線性估計的偏誤階層，提出由偏態區域線性估計式與原本典型的區域線性估計式線性組合而成的估計式。假設真實函數的定義域為有界。在邊界範圍時，因偏態區域線性估計式的偏移點超出邊界，使得此一線性組成的估計式無法運行。針對此一問題，文中提供一個解決的方法。在部分的邊界範圍中，選取適當不對稱的偏移參數，可使其偏誤階層較區域線性估計式的偏誤階層降低一個階層，而不影響變異數的階層。

In this context, we consider the estimator proposed in Choi and Hall (1998), a linear combination of the skewed local linear estimators and a classic local linear estimator. It is used for reducing the bias order of the classic local linear estimator. Assume that the support of the real function is bounded. In the boundary region, the linear combination estimator doesn't work because the shifted points of the skewed local linear estimators are not in the support of the real function. We propose a method to solve this problem. In partial regions near the boundaries, with the proper asymmetric shifted parameters, the bias of the estimator can be reduced by an order of magnitude, compared to the bias of the classic local linear estimator, and the order of magnitude of variance is not influenced.