Econometrica: May 2006, Volume 74, Issue 3

Local Partitioned Regression

https://doi.org/10.1111/j.1468-0262.2006.00683.x
p. 787-817

Norbert Christopeit, Stefan G. N. Hoderlein

In this paper, we introduce a kernel‐based estimation principle for nonparametric models named local partitioned regression (LPR). This principle is a nonparametric generalization of the familiar partition regression in linear models. It has several key advantages: First, it generates estimators for a very large class of semi‐ and nonparametric models. A number of examples that are particularly relevant for economic applications will be discussed in this paper. This class contains the additive, partially linear, and varying coefficient models as well as several other models that have not been discussed in the literature. Second, LPR‐based estimators achieve optimality criteria: They have optimal speed of convergence and are oracle‐efficient. Moreover, they are simple in structure, widely applicable, and computationally inexpensive. A Monte Carlo simulation highlights these advantages.

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Supplemental Material

Supplementary Material to "Local Partitioned Regression"

In this paper we provide additional material on four issues in the main text. The first is an estimator for the covariance matrix Σ in theorem 3.2, precisely defined in (A.15). The second concerns the claim that under our assumptions (3.5) and (3.6) are already implied. The third issue is the calculation of the matrix V in remark 3.3 for general heteroscedasticity. The last issue is the proof of theorem 3.3.

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