Abstract
We all know that we can use the likelihood ratio statistic to test hypotheses and construct confidence intervals in full parametric models. Recently, Owen (1988,Biometrika,75, 237–249; 1990,Ann. Statist.,18, 90–120) has introduced the empirical likelihood method in nonparametric models. In this paper, we combine these two likelihoods together and use the likelihood ratio to construct confidence intervals in a semiparametric problem, in which one model is parametric, and the other is nonparametric. A version of Wilks's theorem is developed.
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References
Lehmann, E. L. (1983).Theory of Point Estimation, New York, Wiley.
Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional,Biometrika,75, 237–249.
Owen, A. B. (1990). Emprical likelihood confidence regions,Ann. Statist.,18, 99–120.
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Qin, J. Semi-empirical likelihood ratio confidence intervals for the difference of two sample means. Ann Inst Stat Math 46, 117–126 (1994). https://doi.org/10.1007/BF00773597
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DOI: https://doi.org/10.1007/BF00773597