Fan, J.Q. and Zhang, J. (2004) Sieve empirical likelihood ratio tests for nonparametric functions. ANNALS OF STATISTICS, 32 (5). pp. 1858-1907. ISSN 0090-5364.
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Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing norparametic hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. We extend their work to the case where the error distribution is completely unspecified via newly proposed sieve empirical likelihood ratio (SELR) tests. The approach is also applied to test conditional estimating equations on the distributions of stochastic errors. It is shown that the proposed SELR statistics follow asymptotically resealed chi(2)-distributions, with the scale constants and the degrees of freedom being independent of the nuisance parameters. This demonstrates that the Wilks phenomenon observed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] continues to hold under more relaxed models and a larger class of techniques. The asymptotic power of the proposed test is also derived, which achieves the optimal rate for nonparametric hypothesis testing. The proposed approach has two advantages over the generalized likelihood ratio method: it requires one only to specify some conditional estimating equations rather than the entire distribution of the stochastic error, and the procedure adapts automatically to the unknown error distribution including heteroscedasticity. A simulation study is conducted to evaluate our proposed procedure empirically.
|Uncontrolled keywords:||nonparametric test; sieve empirical likelihood; conditional estimating equations; Wilks' theorem; varying coefficient models|
|Subjects:||H Social Sciences > HA Statistics|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Judith Broom|
|Date Deposited:||19 Dec 2007 18:22|
|Last Modified:||15 Oct 2012 12:37|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/597 (The current URI for this page, for reference purposes)|
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