删失数据下单指标模型的经验似然推断

Inferences in a Censored Single-index Model with Empirical Likelihood

考虑删失数据下单指标模型,研究了模型中参数的经验似然推断,证明了所提出的调整的经验对数似然比渐近于卡方分布,由此构造相应兴趣参数的置信域.进一步,由于模型中参数向量的范数等于1,利用该约束条件来降低参数的维数,从而增加置信域的精度.模拟研究比较了经验似然方法和正态逼近方法的有限样本性质,从置信域的面积和覆盖概率两方面进行了比较,模拟结果表明经验似然方法优于正态逼近方法.

Empirical likelihood method for single-index models with randomly censored data is investigated. An estimated empirical likelihood for the parameters by using a synthetic data approach is developed. An adjusted empirical log-likelihood ratio function is proven to be asymptotically standard chi-squared, and the corresponding confidence regions of the parame- ters are then constructed. Furthermore, since the index is of norm 1, this constraint is used to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study indicates that compared with a normal approximation method, the proposed method works better in terms of coverage probabilities and areas of confidence regions.