Nonparametric Mixed Ratio Estimator for a Finite Population Total in Stratified Sampling

Abstract

We propose a nonparametric regression approach to the estimation of a finite population total in model based frameworks in the case of stratified sampling. Similar work has been done, by Nadaraya and Watson (1964), Hansen et al (1983), and Breidt and Opsomer (2000). Our point of departure from these works is at selection of the sampling weights within every stratum, where we treat the individual strata as compact Abelian groups and demonstrate that the resulting proposed estimator is easier to compute. We also make use of mixed ratios but this time not in the contexts of simple random sampling or two stage cluster sampling, but in stratified sampling schemes, where a void still exists.