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| 1 | Empirical likelihood confidence regions of the parameters in a partially linear single-index model显示文摘In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method. | XUE Liugen~1 & ZHU Lixing~2 1. College of Applied Sciences,Beijing University of Technology,Beijing 100022,China 2. Department of Mathematics,Hong Kong Baptist University,Hong Kong,China | 2005 | Science China Mathematics2005，48，10： | 13 |
| 2 | Empirical likelihood-based inference in a partially linear model for longitudinal data显示文摘A partially linear model with longitudinal data is considered, empirical likelihood to infer- ence for the regression coefficients and the baseline function is investigated, the empirical log-likelihood ratios is proven to be asymptotically chi-squared, and the corresponding confidence regions for the pa- rameters of interest are then constructed. Also by the empirical likelihood ratio functions, we can obtain the maximum empirical likelihood estimates of the regression coefficients and the baseline function, and prove the asymptotic normality. The numerical results are conducted to compare the performance of the empirical likelihood and the normal approximation-based method, and a real example is analysed. | XUE LiuGen~(1+) & ZHU LiXing~2 1 College of Applied Sciences, Beijing University of Technology, Beijing 100022, China 2 Department of Mathematics, Hong Kong Baptist University, Hong Kong, China | 2008 | Science China Mathematics2008，51，1： | 9 |
| 3 | Empirical likelihood for single-index models with responses missing at random显示文摘The missing response problem in single-index models is studied, and a bias-correction method to infer the index coefficients is developed. Two weighted empirical log-likelihood ratios with asymptotic chisquare are derived, and the corresponding empirical likelihood confidence regions for the index coefficients are constructed. In addition, the estimators of the index coefficients and the link function are defined, and their asymptotic normalities are proved. A simulation study is conducted to compare the empirical likelihood and the normal approximation based method in terms of coverage probabilities and average lengths of confidence intervals. A real example illustrates our methods. | XUE LiuGen LIAN Heng | 2016 | Science China Mathematics2016，59，6： | 2 |
| 4 | Variable selection for single-index varying-coefficient model显示文摘 | Sanying FENG Liugen XUE | 2013 | Frontiers of Mathematics in China2013，8，3： | 2 |
| 5 | Empirical likelihood semiparametric regression analysis for longitudinal data显示文摘 | XUE Liugen ZHU Lixing | 2007 | Biometrika2007，94，： | 1 |
| 6 | Variable selection for partially linear models with randomly censored data显示文摘 | YANG Yiping XUE Liugen CHENG Weihu | 2010 | Communications in Statistics-Simulation and Computation2010，39，： | 1 |
| 7 | Instrumental variable-based empirical likelihood inferences for varying-coefficient models with er-ror-prone covariates 显示文摘 | ZHAO Peixin XUE Liugen | 2013 | Journal of Applied Statistics2013，40，： | 1 |
| 8 | Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition 显示文摘 | ZHANG Weiwei LI Gaorong XUE Liugen | 2011 | Computational Statistics & Data Analysis2011，55，： | 1 |
| 9 | Variable selection for semiparametric varying coefficient partially linear error - in - variables models 显示文摘 | Zhao Peixin Xue Liugen | 2010 | Journal of Multivariate Analysis2010，101，： | 1 |
| 10 | Variable selection for varying coefficient models with measurement errors 显示文摘 | Zhao Peixin Xue Liugen | 2011 | Metrika2011，74，： | 1 |
| 11 | Empirical likelihood for linear models with missing responses显示文摘 | XUE Liugen | | 0，，06： | 1 |
| 12 | Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition显示文摘 | Weiwei Zhang Gaorong Li Liugen Xue | 2011 | Computational Statistics and Data Analysis2011，，11： | 1 |
| 13 | Empirical likelihood for linear models with missing responses 显示文摘 | Liugen Xue | 2009 | Journal of Multivariate Analysis2009，100，7： | 1 |
| 14 | TWO-STEP ESTIMATORS IN PARTIAL LINEAR MODELS WITH MISSING RESPONSE VARIABLES AND ERROR-PRONE COVARIATES显示文摘有失踪的反应变量和错误容易的 covariates 的一个部分线性模型被考虑。归罪途径被开发估计回归系数和 nonparametric 功能。建议参量的评估者被显示 asymptotically 正常,并且为 nonparametric 部分的评估者被证明以最佳的率收敛。到为回归系数和 nonparametric 功能的构造信心区域,分别地,作者也建议 empirical-likelihood-based 统计并且调查实验可能性的比率的限制分布。模拟学习被进行为建议评估者比较有限样品行为。到爱滋病数据集的一个应用程序被说明。 | Yiping YANG Liugen XUE Weihu CHENG | 2011 | Journal of Systems Science & Complexity2011，24，6： | 1 |
| 15 | Empirical likelihood inferences for semiparametric varying-coefficient partially linear errors-in-var- iables models with longitudinal data 显示文摘 | ZHAO Peixin XUE Liugen | 2009 | Journal of Nonparametric Statistics2009，21，7： | 1 |
| 16 | Empirical likelihood for generalized linear models with missing responses显示文摘 | XUE Dong XUE Liugen CHENG Weihu | 2011 | Journal of Statistical Planning and Inference2011，，141： | 1 |
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