Use of Ranked Set Sampling for Estimation of Population Parameters

Abstract

In this dissertation, we first propose an unbiased and efficient proportion estimator using concomitant-based double ranked set sampling (CDRSS) scheme and compare with existing concomitant-based ranked set sampling (CRSS) and simple random sampling (SRS) based counterparts. An application to real data set is also considered to illustrate the procedure. We also propose two families of proportion estimators, that based on ratio method of es timation, under CRSS and CDRSS schemes to minimize loss in precision. The expressions of bias and MSE of these families are derived up to first order of approximation. REs of some particular members of these families are obtained by numerical integration technique using Mathematica Software. An environmental data set is used to support the proposed estimators. The problem of missing data (MD) in estimating population proportion is also addressed. In this connection, some general estimators are introduced for imputation of MD using CRSS scheme in the situation when mean of the continuous concomitant variable is known (unknown). The expressions of bias and mean square error of the suggested estimators are derived up to the first order of approximation along with their gain in accuracy formulae. To assess reliability of the suggested estimators with respect to usual proportion estimator under same missing data scenario, two measures are used (i) gain in accuracy (ii) relative efficiency. The results are obtained by using numerical integration. We also summaries the MD problem under CDRSS scheme. Different methods of estimating sensitive population proportion are also introduced using CRSS schemes and investigate their properties. It is shown that these estimators provide more precise results as oppose to the existing Warner (1965). Finally, some new improved ranked set sampling (RSS) schemes are developed, under perfect and imperfect ranking situations, for estimating population mean and median. We discuss their properties under different distributions. It is observed by numerical studies that the proposed schemes are at least more efficient than SRS scheme in estimating population mean and median.