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在φ混合的随机误差下,本文研究了固定设计及响应变量有缺失的非参数回归模型中回归函数的经验似然置信区间的构造.首先采用非参数回归填补法对缺失的数据进行填补,其次利用补足后得到的"完全样本"构造了非参数回归函数的经验似然比统计量,并证明了经验似然比统计量的极限分布为卡方分布,利用此结果可以构造非参数回归函数的经验似然置信区间.

Empirical Likelihood for Nonparametric Regression Models of varphi Mixing Samples with Missing Data

Under the mixing random errors, we make the empirical likelihood (EL) inference for nonparametric regression models with fixed designs and missing responses. Based on the `complete sample' after nonparametric regression imputation, we show that the EL ratio statistic of the nonparametric regression function is asymptotically $\chi^2$-type distributed, which is used to obtain EL-based confidence intervals for the nonparametric regression function.