On Estimation of Population Coefficient of Variation in Presence of Measurement Errors

Abstract

The present article addresses the effects of measurement errors on the estimation of population coefficient of variation C Y of the study variable Y. Bias and mean squared error (MSE) of the proposed estimator are derived upto the first order of approximation under simple random sampling design. A theoretical efficiency comparison is made between the proposed estimator and the usual coefficient of variation estimator in presence of measurement errors. Based on large sample approximations the optimal condition is obtained under which the proposed estimator performs better than the conventional estimator in presence of measurement errors. Theoretical results are verified by the simulation study using R software.

A general class of improved population variance estimators under non-sampling errors using calibrated weights in stratified sampling

“…and The Percentage Relative Efficiency (PRE) of the proposed estimator T concerning the estimator τ is given by PRE= MSE(τ ) Min.MSE(T) * 100 Where Eqs. ( 8)- (11) give the corresponding equations for Min MSE(T) and MSE(τ ), without or with measurement errors, respectively. ( 6)…”

“…In the presence of random non-response or measurement errors, various researchers have addressed the need for robust estimators 9 . introduced a class of estimators using auxiliary information for estimating finite population variance in the presence of measurement errors, while 10 developed classes of factor-type estimators in the presence of measurement error 11 . focused on the estimation of the population coefficient of variation in the presence of measurement errors, and 12 worked on estimating the population mean in the presence of measurement error and non-response under stratified random sampling 13 .…”

Estimation of Heterogeneous Population Variance using Memory-type Estimators based on EWMA statistic in the presence of Measurement Error for Time-Scaled Surveys

“…MEs may be defined as the difference between the observed values and the true values of the main variable of interest. The use of MEs together with the estimation of unknown population mean is studied by many authors including Singh and Karpe (2009), Misra et al (2017), Khalil et al (2018Khalil et al ( , 2019, Zahid and Shabbir (2019) and . Many researchers like Singh and Karpe (2008), Diana and Giordan (2012), Sharma and Singh (2013), Misra et al (2016), Masood and Shabbir (2016), Singh and Pal (2016), and Tariq et al (2021) suggested improved estimators for the estimation of population variance in the presence of MEs.…”

Memory-type variance estimators using exponentially weighted moving average statistic in presence of measurement error for time-scaled surveys

“…Many authors have studied the effect of ME along with the estimation of population parameters. One may refer to [13][14][15][16][17][18]. Several researchers like [19][20][21][22][23][24] contribute to the variance estimation of the concerned variable in the presence of ME.…”