Jackknife Empirical Likelihood Of Error Variance For Partially Linear Varying-Coefficient Model With Missing Covariates
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS(2023)
Abstract
In this paper, we apply the profile least-square method and inverse probability weighted method to define estimation of the error variance in partially linear varying-coefficient model when the covariates are missing at random. At the same time, we construct a jackknife estimator and jackknife empirical likelihood (JEL) statistic of the error variance, respectively. It is proved that the proposed estimators are asymptotical normality and the JEL statistic admits a limiting standard chi-square distribution. A simulation study is conducted to compare the JEL method with the normal approximation approach in terms of coverage probabilities and average interval lengths, and a comparison of the proposed estimators is done based on sample means, biases and mean square errors under different settings. Subsequently, a real data set is analyzed for illustration of the proposed methods.
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Key words
Asymptotically normal, error variance, Jackknife empirical likelihood, missing at random, partially linear varying-coefficient model
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