Two-step semiparametric empirical likelihood inference Articles uri icon

publication date

  • February 2020

start page

  • 1

end page

  • 26


  • 1


  • 48

International Standard Serial Number (ISSN)

  • 0090-5364

Electronic International Standard Serial Number (EISSN)

  • 0003-4851


  • In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks" theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks" theorem breaks down. This article suggests a general approach to restore Wilks" phenomenon in two-step semiparametric empirical likelihood inferences. The main insight consists in using as the moment function in the estimating equation the influence function of the plug-in sample moment. The proposed method is general; it leads to a chi-squared limiting distribution with known degrees of freedom; it is efficient; it does not require undersmoothing; and it is less sensitive to the first-step than alternative methods, which is particularly appealing for high-dimensional settings. Several examples and simulation studies illustrate the general applicability of the procedure and its excellent finite sample performance relative to competing methods


  • Economics


  • empirical likelihood, high-dimensional parameters, semiparametric inference, wilks’ phenomenon