A CLASS of REGRESSION-CUM-RATIO ESTIMATORS in TWO-PHASE SAMPLING for UTILIZING INFORMATION from HIGH RESOLUTION SATELLITE DATA

Abstract

Two-phase sampling design offers a variety of possibilities for effective use of auxiliary information such as those from high resolution remote sensing data. Continuous satellite data with large area coverage provide scope for deriving population values of the auxiliary variables, which can effectively be used for estimating the population parameters of the variable of interest. This study has been made to examine the possibilities of different forms of auxiliary information derived from remote sensing data in two-phase sampling design and suggest an appropriate estimator that will be of broad interest and applications. A new class of regression-cum-ratio estimators has been proposed for two-phase sampling using information on two auxiliary variables derived from high resolution satellite data. The bias and the mean square error (MSE) of the proposed estimators have been obtained up to first order approximation. Efficiency comparison of the proposed estimators has been made with some traditional estimators. The proposed estimator is found to be more efficient than the usual regression and ratio estimators. Numerical illustration has been carried out to examine the efficiency of the estimator in case of forest timber volume estimation utilizing tree crown diameter and tree height as auxiliary variables. It is shown that these estimators can be employed in a variety of conditions where there is strong correlation of satellite derived information with sample based ground measurements and when the cost of ground measurements is relatively high.