Local piecewise linear regression

In this paper, we propose a new nonparametric estimator called the local pi ecewise linear regression estimator. The proposed estimator has the advanta ges of the regression spline and the local linear regression estimator but overcomes the drawbacks of both. Here we study the asymptotic behavior of t he proposed estimator. Under suitable conditions, we derive the leading bia s and variance terms of the local piecewise linear regression estimator at the interior and boundary points for both the fixed design and the random d esign. As a result, we are able to see clearly many optimal properties of t he local piecewise linear regression estimator. For example, the proposed e stimator is efficient, design-adaptive and computationally inexpensive, and it suffers no boundary effects.