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SEMI-EMPIRICAL LIKELIHOOD RATIO CONFIDENCE INTERVALS

FOR THE DIFFERENCE OF TWO SAMPLE MEANS

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JING QIN

*Department of Statistics and Actuarial Science, University of Waterloo,*

Waterloo, Ontario, Canada N2L 3G1
(Received February 18, 1993; revised June 2, 1993)

**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.

*Key words and phrases*:
Empirical likelihood, hypotheses
tests, semi-empirical likelihood, Wilks's theorem.

**Source**
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