摘要
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.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2012年第2期297-311,共15页
Acta Mathematica Scientia
基金
国家社科基金(11CTJ004)
国家自然科学基金(11126332
11101452)
重庆市自然科学基金(CSTC2011JJA00014)
重庆市教委科学技术研究项目(KJ110720)
北京市自然科学基金(1102008)
广西自然科学基金(2010GXNSFB013051)资助
关键词
删失数据
单指标模型
经验似然
χ~2分布
Censored data
Single-index model
Empirical likelihood
χ2-distribution.