删失数据下非线性半参数回归模型中参数的经验似然推断

Empirical Likelihood Inference of Parameters in a Censored Nonlinear Semiparametric Regression Model

考察了响应变量在随机删失情形下的非线性半参数回归模型,构造了未知参数的经验对数似然比统计量和调整经验对数似然比统计量,证明在一定条件下,所构造的经验似然比统计量渐近于X^2分布,并由此构造出未知参数的置信域.此外,又构造了未知参数的最小二乘估计量,证明了它的渐近性质.通过模拟研究表明,经验似然方法在置信域的覆盖概率以及精度方面要优于最小二乘法.

In this paper, a censored nonlinear semiparametric regression model is investigated. Empirical log-likelihood ratio statistics and adjust empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is shown that the proposed statistics have asymptotically ehi-squared distribution under some mild conditions, and hence it can be used to construct the confidence region of the unknown parameter. In addition the least squares estimator of unknown parameter is constructed, and its asymptotic behavior is proved. A simulation study is carried out to show the empirical likelihood methods appears to be better than the least-squares method in terms of the confidence regions and its coverage probabilities.