Linearity testing using local polynomial approximation

Hjellvik, V. and Yao, Qiwei and Tjostheim, D. (1998) Linearity testing using local polynomial approximation. Journal of Statistical Planning and Inference, 68 (2). pp. 295-321. ISSN 0378-3758. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We use local polynomial approximation to estimate the conditional mean and conditional variance, and test linearity by using a functional measuring the deviation between the nonparametric estimates and the parametric estimates based on a linear model. We also employ first- and second-order derivatives for this purpose, and we point out some advantages of using local polynomial approximation as opposed to kernel estimation in the context of linearity testing. The asymptotic theory of the test functionals is developed in some detail for a special case. It is used to draw qualitative conclusions concerning the bandwidth, but in order to apply the asymptotic distribution to specific testing problems very large sample sizes are needed. For moderate sample sizes we have examined a bootstrap alternative in a large variety of situations. We have tried bandwidths suggested by asymptotic results as well as bandwidths obtained by cross-validation.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: R.F. Xu
Date Deposited: 09 Jul 2009 09:50
Last Modified: 25 Jun 2014 14:13
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