A Correction Note on Improvement in Variance Estimation Using Auxiliary Information

Abstract

Shabbir and Gupta (2007) introduced an exponential ratio-type estimator for the population variance and compare its mean square error with mean square error of some of the existing estimators. But unfortunately, the expression of mean square error of their proposed estimator is incorrect and hence the comparison based on incorrect mean square error, carried by them, is wrong. In the present article, the author provides the correct expression of the mean square error, up to first order of approximation, of the same estimator. A comparison has been made by taking the corrected expression of mean square error. The corresponding exponential ratiotype estimator for the population variance, under double sampling technique, is also proposed which followed by a comparison.

Generalized Estimators for Finite Population Variance Using Measurable and Affordable Auxiliary Character

“…As a result, researchers are keen in the variability associated with their products. The issue of constructing efficient population variance estimators with higher predictive ability has been discussed by various authors such as Liu [38], Das & Tripathi [39], Grover [40], Isaki [41], Upadhaya & Singh [42], Singh & Singh [43], Ahmed et al [44], Al-Jararha & Ahmed [45], Ahmed et al [46], Kadilar & Cingi [47], Bahl & Tuteja [48], Upadhyaya et al [49], Ahmed and Singh [50], Swain [51], Subramani & Kumarapandiyan [52], Shabbir & Gupta [53], Singh & Malik [54], Yadav et al [55], Yadav & Kadilar [66], Ahmed et al [12,18], Muili et al [57,[58][59][60]. The aforementioned authors had worked on variance estimation under different sampling procedures.…”

Generalized Regression-Cum-Exponential Estimators Using Two Auxiliary Variables for Population Variance in Simple Random Sampling

“…[7] utilized a single auxiliary variable to propose an estimator in population variance and provide more efficient results as compare to the ratio estimator. The studies related to the estimation of population variance have made by different authors such as [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

A Generalised Family of Estimator for Estimating Unknown Variance Using Two Auxiliary Variables

“…If information on an auxiliary variable is readily available then it is a well-known fact that the ratio-type and regression-type estimators can be used for estimation of parameters of interest, due to increase in efficiency of these estimators. The problem of estimating the population variance of S y 2 of study variable y received a considerable attention of the statistician in survey sampling including [2], [3], [4], [5][6][7], [12], [13], [14], [15][16], [20] and [18] and have suggested improved estimators for estimation of S y 2 let ϕ i (i=1,2,……..,N) be the population having N units such that y is highly correlated with the auxiliary variables x and z. We assume that a simple random sample without replacement (SrSWOr) of size n is drawn from the finite population of size N. let ( ' , ' ) ( , and be the population variances of variables x, z and y respectively.…”