An alternative to ratio method in sample surveys

Abstract

SummaryThis paper examines a simple transformation which enables the use of product method in place of ratio method. The convenience with the former, proposed by Murthy [3], is that expressions for bias and mean square error (mse) can be exactly evaluated. The optimum situation in the minimum mse sense and allowable departures from this optimum are indicated. The procedure requires a good guess of a certain parameter, which does not seem very restrictive for practice. Two methods for dealing with the bias of the estimator are mentioned. An extension to use multiauxiliary information is outlined.

On linear regression and ratio-product estimation of a finite population mean

“…However, in repeated surveys or studies based on multiphase sampling, where information regarding the same variates is collected on several occasions, it is possible to estimate quite accurately the values of certain parameters such as C y , C x and ρ. This problem has been studied among others by Murthy (1967), pages 96-99, Reddy (1978) and Srivenkataramana and Tracy (1980). Thus the value of C can be estimated quite accurately, and such an estimate can be used in practice.…”

An improved class of estimators for the population mean

“…To the first order of approximation, all these sub-classes reduce to the regression estimator in the optimum case both when the parameters are assumed known or must be estimated. In addition, out of the Naik and Gupta class, we mention Srivastava (1971); Gupta (1978); Sahai and Ray (1980); Srivastava (1980); Srivenkataramana and Tracy (1980); Ray and Sahai (1980); Pandey (1980); Singh and Shukla (1987); Sampath and Durairajan (1988); Singh and Espejo (2003).…”

A Class of Estimators for Estimating the Variance of the Ratio Estimator

“…It may be noted that even if the values of the constants used in estimator are not exactly equal to their optimum values as given by (3.6) but are close enough, the resulting estimator will be more efficient than the usual estimator V 0 . For further discussion on this subject the reader is referred to Srivastava (1966), Tripathi (1978), Das and Tripathi (1978), Srivenkataramana and Tracy (1980) and Singh (2003).…”