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Empirical likelihood of conditional quantile difference with left-truncated and dependent data
Kong Cui-Juan,Liang Han-Ying 한국통계학회 2020 Journal of the Korean Statistical Society Vol.49 No.4
We, in this paper, apply the smoothed and maximum empirical likelihood (EL) methods to construct the confdence intervals of the conditional quantile diference with left-truncated data. In particular, we prove the smoothed empirical log-likelihood ratio of the conditional quantile diference is asymptotically chi-squared when the observations with multivariate covariates form a stationary 훼-mixing sequence. At the same time, we establish the asymptotic normality of the maximum EL estimator for the conditional quantile diference. A simulation study is conducted to investigate the fnite sample behavior of the proposed methods and a real data application is provided.