Pseudo‐empirical likelihood ratio confidence intervals for complex surveys

The authors show how an adjusted pseudo-empirical likelihood ratio statistic that is asymptoti- cally distributed as a chi-square random variable can be used to construct confidence intervals for a finite population mean or a finite population distribution function from complex surv ey samples. They consider both non-stratified and stratified sampling designs, with or without auxiliary in formation. They examine the behaviour of estimates of the mean and the distribution function at specifi c points using simulations calling on the Rao-Sampford method of unequal probability sampling without replacement. They conclude that the pseudo-empirical likelihood ratio confidence intervals are super ior to those based on the normal approximation, whether in terms of coverage probability, tail error rates or average length of the intervals.

[1]  M. Sampford,et al.  On sampling without replacement with unequal probabilities of selection. , 1967, Biometrika.

[2]  J. Rao,et al.  EMPIRICAL LIKELIHOOD INFERENCE UNDER STRATIFIED RANDOM SAMPLING USING AUXILIARY INFORMATION , 2002 .

[3]  Xiaotong Shen,et al.  Empirical Likelihood , 2002 .

[4]  J. A. Vísek.  Asymptotic Distribution of Simple Estimate for Rejective, Sampford and Successive Sampling , 1979 .

[5]  Changbao Wu,et al.  Algorithms and R Codes for the Pseudo Empirical Likelihood Method in Survey Sampling , 2005 .

[6]  Randy R. Sitter,et al.  A PSEUDO EMPIRICAL LIKELIHOOD APPROACH TO THE EFFECTIVE USE OF AUXILIARY INFORMATION IN COMPLEX SURVEYS , 1999 .

[7]  C. T. Isaki,et al.  Survey Design under the Regression Superpopulation Model , 1982 .

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

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

[10]  Wu.  Using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys , 2002 .

[11]  Changbao Wu,et al.  Combining Information from Multiple Surveys through the Empirical Likelihood Method , 2022 .

[12]  J. Hájek.  Asymptotic Theory of Rejective Sampling with Varying Probabilities from a Finite Population , 1964 .

[13]  J. N. K. Rao,et al.  Empirical likelihood inference under stratified random sampling using auxiliary population information , 2000 .

[14]  Changbao Wu,et al.  SOME ALGORITHMIC ASPECTS OF THE EMPIRICAL LIKELIHOOD METHOD IN SURVEY SAMPLING , 2004 .

[15]  Changbao Wu,et al.  ESTIMATION OF DISTRIBUTION FUNCTION AND QUANTILES USING THE MODEL-CALIBRATED PSEUDO EMPIRICAL LIKELIHOOD METHOD , 2002 .

[16]  J. Rao,et al.  Inference From Stratified Samples: Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods , 1981 .