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Empirical likelihood for partial linear models with fixed designs

โœ Scribed by Qi-Hua Wang; Bing-Yi Jing


Book ID
104303011
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
378 KB
Volume
41
Category
Article
ISSN
0167-7152

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โœฆ Synopsis


The empirical likelihood method of Owen [Owen, A., 1988. Empirical likelihood ratio confidence intervals for single functional. Biometrika 75, 237-249], is extended to partial linear models with fixed designs in this paper. A nonparametric version of Wilks' theorem is derived. The result is then used to construct confidence regions of the parameter vector in the partial linear models with asymptotically correct coverage probabilities.


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In this paper, we consider the application of the empirical likelihood method to partially linear model. Unlike the usual cases, we first propose an approximation to the residual of the model to deal with the nonparametric part so that Owen's (1990) empirical likelihood approach can be applied. Then

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Consider the partial linear model Y i =X { i ;+ g(T i )+= i , i=1, ..., n, where ; is a p\_1 unknown parameter vector, g is an unknown function, X i 's are p\_1 observable covariates, T i 's are other observable covariates in [0, 1], and Y i 's are the response variables. In this paper, we shall con