Empirical likelihood inference with public-use survey data (Q2192309)

Empirical Likelihood approach was first introduced by \textit{H. O. Hartley} and \textit{J. N. K. Rao} [Ann. Math. Stat. 33, 350--374 (1962; Zbl 0121.13704)], termed as `scale load likelihood' in the context of sampling from finite population. This was later proposed for inference from i.i.d. samples by \textit{A. B. Owen} [Biometrika 75, No. 2, 237--249 (1988; Zbl 0641.62032)]. Methods later developed by a host of researchers required detailed design information and availability of related auxiliary information for inference using calibration constraints. However, in actual practice, public use survey data as a source of data for researchers in social sciences and health studies consists of data sets related to several variables of interest and final survey weights. In this paper, the authors present empirical likelihood methods under such a scenario. Two approaches, namely pseudo empirical likelihood (PEL) and sample empirical likelihood (SEL) are considered. Since public use survey data is collected on several variables, it is desirable to first make a variable selection. For this, PEL and SEL provide design based approach to variable selection through a penalized PEL or SEL approaches. A simulation study and an application to general Social Survey (GSS) 2016 of Canada show that the proposed methods fare well under different scenarios. Canadian GSS 2016 collected information on life style behavior that affects health and well-being of Canadians at work place and private homes. An appendix at the end gives theoretical justification for bootstrap calibrated empirical likelihood methods.