Modified Calibration Variance Estimators in the Presence of Non- response and Measurement Error
Z. Abubakar
Department of Statistics, Usmanu Danfodiyo University, Sokoto, Nigeria.
A. Audu
Department of Statistics, Usmanu Danfodiyo University, Sokoto, Nigeria.
L. Kane
Department of Statistics, Usmanu Danfodiyo University, Sokoto, Nigeria.
A. M. Dogondaji
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.
M. A. Yunusa *
Department of Statistics, Usmanu Danfodiyo University, Sokoto, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Samples from a population that can be divided into smaller groups are taken using a technique called stratified sampling. When subpopulations within the total population differ, it may be beneficial to sample each stratum (subpopulation) separately in sample surveys. Government organizations, independent consultants, and applied statisticians all frequently use this crucial strategy. There are many problems encountered by survey statisticians in estimating the population variance of the study variable. These problems include the presence of outliers in data collected for analysis, non-response, and measurement errors occurring during the survey. Shahzad et al. [1] developed variance estimators by addressing the problem of outliers using the L-moment and calibration approach. However, they do not consider the situation of non-response and measurement errors. This paper addresses these problems by proposing modified variance estimators in the presence of non-response and measurement errors. The properties (Biases and MSEs) were derived up to the first order of approximation using the Taylor series approach. The efficiency conditions of the modified estimators over the existing estimators considered in the study were established. The result of simulation studies revealed that the estimators are efficient.
Keywords: MSE, bias, calibration variance estimator, measurement error, non-response