Empirical likelihood estimation for a single-index varying-coefficient model

来源 :IMS-China International Conference on Statistics and Probabi | 被引量 : 0次 | 上传用户:xiaoliang1978
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  In this paper, local empirical likelihood-based inference for a varying coefficicnt model with longitudinal data is investigated.First, we show that the naive empiri cal likelihood ratio is asymptotically chi-squared when undersmoothing is employed.The ratio is self-scale invariant, and the plug-in estimation of the limiting variance is not needed.Second, to enhance the performance of the ratio, mean-corrected and residual-adjusted empirical likelihood ratios are recommended.The merit of these two bias corrections is that without undersmoothing, both also have chi-square lim its.Third, a maximum empirical likelihood estimator (MELE) of the time-varying coefficient is defined, the asymptotic equivalence to the weighted least-squares es timator (WLSE) is provided, and the asymptotic normality is shown.By the em pirical likelihood ratios and the normal approximation of the MELE/WLSE, the confidence regions of the time-varying coefficients are constructed.Fourth, when some components arc of particular interest, we suggest mean-corrected and residual adjusted partial empirical likelihood ratios for thc construction of the confidence regions/intervals.In addition, we also consider the constructions of the simultane ous and bootstrap confidence bands.A simulation study is undertaken to compare the empirical likelihood, the normal approximation and the bootstrap methods in terms of coverage accuracies and average areas/widths of confidence regions/bands.An example in epidemiology is used for illustration.
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