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- Title
Sieve Empirical Likelihood and Extensions of the Generalized Least Squares.
- Authors
Zhang, J.; Gijbels, I.
- Abstract
The empirical likelihood cannot be used directly sometimes when an infinite dimensional parameter of interest is involved. To overcome this difficulty, the sieve empirical likelihoods are introduced in this paper. Based on the sieve empirical likelihoods, a unified procedure is developed for estimation of constrained parametric or non–parametric regression models with unspecified error distributions. It shows some interesting connections with certain extensions of the generalized least squares approach. A general asymptotic theory is provided. In the parametric regression setting it is shown that under certain regularity conditions the proposed estimators are asymptotically efficient even if the restriction functions are discontinuous. In the non–parametric regression setting the convergence rate of the maximum estimator based on the sieve empirical likelihood is given. In both settings, it is shown that the estimator is adaptive for the inhomogeneity of conditional error distributions with respect to predictor, especially for heteroscedasticity.
- Subjects
LEAST squares; MOMENTS method (Statistics); REGRESSION analysis; MATHEMATICAL statistics
- Publication
Scandinavian Journal of Statistics, 2003, Vol 30, Issue 1, p1
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/1467-9469.t01-1-00315