Parameter Estimation in Case of Incomplete Frames using Ratio Estimators

Shilpa  Yadav; Pankaj  Nagar

Authors

Shilpa Yadav Department of Statistics, University of Rajasthan, Jaipur, Rajasthan, India
Pankaj Nagar Department of Statistics, University of Rajasthan, Jaipur, Rajasthan, India

Keywords:

Incomplete sampling frame, double sampling, ratio method of estimation, predecessor-successor method, ancillary variable

Abstract

Existence of a well defined and perfect sampling frame is the fundamental requirement of any
sample survey. But there is enough evidence to support the fact that a perfect sampling frame that
captures all the individual units of the population is rarely available, especially for a dynamic population where a constant movement of the units of the population is observed. In such cases, the sample
collected can not be considered as a good representative of the population and the problem of incomplete frame arises. The results so drawn can immensely change the survey results and influence the legitimacy of the research. This study deals with the incomplete frame problem using ratio method of estimation, where the information on the auxiliary or ancillary variable is collected in the first phase and a second phase sample is then drawn to obtain estimates of the population mean of the characteristic under study and its mean square error up to first order approximation. Two different estimators, viz., combined ratio estimator and separate ratio estimators have been used and their efficiencies are compared. Further, the results are illustrated numerically with the help of Monte-Carlo simulations.

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