Split sample empirical likelihood

We propose a new approach that combines multiple non-parametric likelihood-type components to build a data-driven approximation of the true likelihood function. Our approach is built on empirical likelihood, a non-parametric approximation of the likelihood function. We show the asymptotic behaviors of our approach are identical to those seen in empirical likelihood. We demonstrate that our method performs comparably to empirical likelihood while significantly decreasing computational time.

[1]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[2]  N. Reid,et al.  AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS , 2011 .

[3]  Jian Shi,et al.  Empirical Likelihood for Partially Linear Models , 2000 .

[4]  P. J. Huber.  Robust Estimation of a Location Parameter , 1964 .

[5]  G. Box.  Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification , 1954 .

[6]  F. Lindsten,et al.  Divide-and-Conquer With Sequential Monte Carlo , 2014, 1406.4993.

[7]  J. F. Lawless,et al.  Estimating equations, empirical likelihood and constraints on parameters† , 1995 .

[8]  Ronald D. Snee,et al.  Validation of Regression Models: Methods and Examples , 1977 .

[9]  A. Owen.  Empirical likelihood ratio confidence intervals for a single functional , 1988 .

[10]  Art B. Owen,et al.  Empirical Likelihood for Linear Models , 1991 .

[11]  J. Lawless,et al.  Empirical Likelihood and General Estimating Equations , 1994 .

[12]  F. Liang,et al.  A split‐and‐merge Bayesian variable selection approach for ultrahigh dimensional regression , 2015 .

[13]  A. Owen.  Empirical Likelihood Ratio Confidence Regions , 1990 .

[14]  Yuichi Kitamura,et al.  Empirical likelihood methods with weakly dependent processes , 1997 .

[15]  Harry Joe,et al.  Composite Likelihood Methods , 2012 .

[16]  Jiahua Chen,et al.  Empirical likelihood estimation for ?nite populations and the e?ective usage of auxiliary informatio , 1993 .

[17]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[18]  Thomas J. DiCiccio,et al.  Empirical Likelihood is Bartlett-Correctable , 1991 .

[19]  N. Lazar.  Bayesian empirical likelihood , 2003 .

[20]  Minge Xie,et al.  A Split-and-Conquer Approach for Analysis of Extraordinarily Large Data , 2014 .

[21]  George G. Judge,et al.  Revised empirical likelihood , 2010 .

[22]  Biao Zhang,et al.  Empirical‐likelihood‐based inference in missing response problems and its application in observational studies , 2007 .

[23]  Nicole A. Lazar,et al.  Empirical likelihood in the presence of nuisance parameters , 1999 .