Constrained Nonparametric regression

Research Report SRR95-041

Constrained Nonparametric regression

Prakash Patil and Paul L. Speckman

Abstract: Consider a regression function whose general functional form is unknown but which is known to pass through the origin. Nonparametric estimators such as the Nadaraya-Watson type kernel method can provide a `reasonable' estimator of a regression function as a whole, but they do not satisfy the constraint at the origin. Further, if the origin is at the boundary of the design density, then many kernel estimators not only fail to satisfy the constraint but also have higher order bias at the origin than in the interior. There are methods to improve the bias at the boundary including special boundary kernels, but these estimators do not satisfy constraints. In this article we propose a method based on a semiparametric approach to modify the usual kernel estimator so as to satisfy such a constraint without losing the structure and appealing statistical properties of the kernel estimator in the interior.

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