Empirical likelihood inference for estimating equation with missing data. (English) Zbl 1273.62078
Summary: Empirical likelihood inference for estimating equations with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chi-square distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator \(\hat {\theta}\) is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.
MSC:
| 62G05 | Nonparametric estimation |
| 62G15 | Nonparametric tolerance and confidence regions |
| 62G20 | Asymptotic properties of nonparametric inference |
| 65C60 | Computational problems in statistics (MSC2010) |
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