Abstract

This article describes the problem of estimation of finite population mean in two-phase stratified random sampling. Using information on two auxiliary variables, a class of product to regression chain type estimators has been proposed and its characteristic is discussed. The unbiased version of the proposed class of estimators has been constructed and the optimality condition for the proposed class of estimators is derived. The efficacy of the proposed methodology has been justified through empirical investigations carried over the data set of natural population as well as the data set of artificially generated population. The survey statistician may be suggested to use it.

Highlights

  • In this present paper we have made use of Auxiliary information extracted from the variables having correlation with study variable

  • Information on auxiliary variable may be readily available for all the units of population; for example, tonnage of each vehicle or ship is known in survey sampling of transportation and number of beds available in different hospitals may be known well in advance in health care surveys

  • Encouraged with the above work, we have proposed a class of product to regression chain type estimators in stratified sampling using two auxiliary variables under double sampling

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Summary

Introduction

In this present paper we have made use of Auxiliary information extracted from the variables having correlation with study variable. Information on auxiliary variable may be readily available for all the units of population; for example, tonnage (or seat capacity) of each vehicle or ship is known in survey sampling of transportation and number of beds available in different hospitals may be known well in advance in health care surveys. In socio-economic surveys, people may live in rural areas, urban localities, ordinary domestic houses, hostels, hospitals and jail, etc In such a situation one should carefully study the population according to the characteristics of regions and apply sampling scheme strata wise independently. Encouraged with the above work, we have proposed a class of product to regression chain type estimators in stratified sampling using two auxiliary variables under double sampling. The dominance of the proposed estimation strategy over the conventional ones has been established through empirical investigations carried over the data set of natural as well as artificially generated population

Sampling structures and notations
Discussion on existing estimation strategies
Formulation of proposed estimation strategy
Bias and mean square errors of the proposed class of estimator tp
Bias reduction for the proposed class of estimators
Zh zh s2x
Minimum variance of proposed class of estimators
Empirical investigations through natural populations
Findings
Empirical investigations through artificially generated population
Conclusion
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