Noname manuscript No. (will be inserted by the editor) A Review on Empirical Likelihood Methods for Regression Song Xi Chen.Ingrid Van Keilegom Received:date Accepted:date Abstract We provide a review on the empirical likelihood method for regression type inference problems.The regression models considered in this review include parametric, semiparametric and nonparametric models.Both missing data and censored data are accommodated. Keywords Censored data:empirical likelihood;missing data;nonparametric regression;parametric regression;semiparametric regression;Wilks'theorem. 1 Introduction It has been twenty years since Art Owen published his seminal paper(Owen,1988)that introduces the notion of empirical likelihood (EL).Since then,there has been a rich body of literature on the novel idea of formulating versions of nonparametric likelihood in various settings of statistical inference.There have been two major reviews on the empirical likelihood.The first review was given by Hall and La Scala (1990)in the early years of the EL method,which summarized some key properties of the method. The second one was the book by the inventor of the methodology (Owen,2001),which provided a comprehensive overview up to that time. The body of empirical likelihood literature is increasing rapidly,and it would be a daunting task to review the entire field in one review paper like this one.We therefore decided to concentrate our review on regression due to its prominence in statistical S.X.Chen Department of Statistics,lowa State University,Ames,Iowa 50011-1210,USA and Guanghua School of Management,Peking University,China Tel.:1-515-2942729 Fax:1-515-2944040 E-mail:songchen@iastate.edu;csx@gsm.pku.edu.cn I.Van Keilegom Institute of Statistics,Universite catholique de Louvain,Voie du Roman Pays 20,1348 Louvain- la-Neuve,Belgium TeL.:+3210474330 Fax:+3210473032 E-mail:ingrid.vankeilegom@uclouvain.beNoname manuscript No. (will be inserted by the editor) A Review on Empirical Likelihood Methods for Regression Song Xi Chen · Ingrid Van Keilegom Received: date / Accepted: date Abstract We provide a review on the empirical likelihood method for regression type inference problems. The regression models considered in this review include parametric, semiparametric and nonparametric models. Both missing data and censored data are accommodated. Keywords Censored data; empirical likelihood; missing data; nonparametric regression; parametric regression; semiparametric regression; Wilks’ theorem. 1 Introduction It has been twenty years since Art Owen published his seminal paper (Owen, 1988) that introduces the notion of empirical likelihood (EL). Since then, there has been a rich body of literature on the novel idea of formulating versions of nonparametric likelihood in various settings of statistical inference. There have been two major reviews on the empirical likelihood. The first review was given by Hall and La Scala (1990) in the early years of the EL method, which summarized some key properties of the method. The second one was the book by the inventor of the methodology (Owen, 2001), which provided a comprehensive overview up to that time. The body of empirical likelihood literature is increasing rapidly, and it would be a daunting task to review the entire field in one review paper like this one. We therefore decided to concentrate our review on regression due to its prominence in statistical S.X. Chen Department of Statistics, Iowa State University, Ames, Iowa 50011-1210, USA and Guanghua School of Management, Peking University, China Tel.: 1-515-2942729 Fax: 1-515-2944040 E-mail: songchen@iastate.edu; csx@gsm.pku.edu.cn I. Van Keilegom Institute of Statistics, Universit´e catholique de Louvain, Voie du Roman Pays 20, 1348 Louvain￾la-Neuve, Belgium Tel.: +32 10 47 43 30 Fax : +32 10 47 30 32 E-mail: ingrid.vankeilegom@uclouvain.be