TY - JOUR T1 - Semi-Empiricial Likelihood Confidence Intervals for the Differences of Two Populations Based on Fractional Imputation AU - Bai , Yunxia AU - Qin , Yongsong AU - Wang , Lirong AU - Li , Ling JO - Communications in Mathematical Research VL - 2 SP - 123 EP - 136 PY - 2021 DA - 2021/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19297.html KW - empirical likelihood, confidence intervals, fractional imputation, missing data. AB -

Suppose that there are two populations $x$ and $y$ with missing data on both of them, where $x$ has a distribution function $F(·)$ which is unknown and $y$ has a distribution function $G_θ(·)$ with a probability density function $g_θ(·)$ with known form depending on some unknown parameter $θ$. Fractional imputation is used to fill in missing data. The asymptotic distributions of the semi-empirical likelihood ration statistic are obtained under some mild conditions. Then, empirical likelihood confidence intervals on the differences of $x$ and $y$ are constructed.