Localpiecewise linear regression

In this paper, we propose a new nonparametric estimator called the local piecewise linear regression estimator. The proposed estimator has the advantages of the regression spline and the local linear regression estimator but overcomes the drawbacks of both. Here we study the asymptotic behavior of the proposed estimator. Under suitable conditions, we derive the leading bias and variance terms of the local piecewise linear regression estimator at the interior and boundary points for both the fixed design and the random design. As a result, we are able to see clearly many optimal properties of the local piecewise linear regression estimator. For example, the proposed estimator is efficient, designadaptive and computationally inexpensive, and it suffers no boundary effects.