Empirical likelihood of conditional quantile difference with left-truncated and dependent data

• Published in: Journal of the Korean Statistical Society Vol. 49; no. 4; pp. 1106 - 1130
• Main Authors: Kong, Cui-Juan, Liang, Han-Ying
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.12.2020; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Mathematics and Statistics; Research Article; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; Truncated data; 62N02; Asymptotic normality; mixing; Empirical likelihood; 62G20; conditional quantile difference
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1007/s42952-019-00045-5

We, in this paper, apply the smoothed and maximum empirical likelihood (EL) methods to construct the confidence intervals of the conditional quantile difference with left-truncated data. In particular, we prove the smoothed empirical log-likelihood ratio of the conditional quantile difference is asymptotically chi-squared when the observations with multivariate covariates form a stationary α -mixing sequence. At the same time, we establish the asymptotic normality of the maximum EL estimator for the conditional quantile difference. A simulation study is conducted to investigate the finite sample behavior of the proposed methods and a real data application is provided.