A New Class of L-Moments Based Calibration Variance Estimators

Abstract

Variance is one of the most important measures of descriptive statistics and commonly used for statistical analysis. The traditional second-order central moment based variance estimation is a widely utilized methodology. However, traditional variance estimator is highly affected in the presence of extreme values. So this paper initially, proposes two classes of calibration estimators based on an adaptation of the estimators recently proposed by Koyuncu and then presents a new class of L-Moments based calibration variance estimators utilizing L-Moments characteristics (L-location, Lscale, L-CV) and auxiliary information. It is demonstrated that the proposed L-Moments based calibration variance estimators are more efficient than adapted ones. Artificial data is considered for assessing the performance of the proposed estimators. We also demonstrated an application related to apple fruit for purposes of the article. Using artificial and real data sets, percentage relative efficiency (PRE) of the proposed class of estimators with respect to adapted ones are calculated. The PRE results indicate to the superiority of the proposed class over adapted ones in the presence of extreme values. In this manner, the proposed class of estimators could be applied over an expansive range of survey sampling whenever auxiliary information is available in the presence of extreme values.

L-Moments and calibration based variance estimators under double stratified random sampling scheme: an application of covid-19 pandemic

“…Hence, it is recommended to use proposed estimators in the presence of extreme observations. We would like to mention that some other estimators can also be derived in the forthcoming studies by adding the suitable calibration constraints based on L-Moments characteristics of auxiliary information, such as L-Moments based coefficient of variation or skewness of the auxiliary variable, to the proposed estimators given here, as in the studies of Shahzad et al [8].…”

“…Such sort of linear relationship allows researchers to use auxiliary variable X for improved estimation of any parameter of study variable Y . For more discussion on auxiliary information, interested readers may refer to Koyuncu [1], Al-Omari [2], Zaman [3,4], Naz et al [5,6], and Shahzad et al [7,8]. An alternative method for the situations in which an abundance of auxiliary information is available is ranked set sampling due to McIntyre [9].…”

Mean Estimators Using Robust Quantile Regression and L-Moments’ Characteristics for Complete and Partial Auxiliary Information

“…L-moments' are more robust in this situation when extreme values or outliers' spike occurs in the resulting curve of the data. For any random variable that exists with mean, the L-moments are defined as expectations of specific linear combinations of order statistics [7]. Hosking in 19 th century formed the basis of a general theory about L-moments that is summarizing and describing theoretical probability distributions, summarizing and describing samples of observed data, estimating parameters and quantities, and hypothesizing tests of distributions.…”

L-Moments Based Calibrated Variance Estimators Using Double Stratified Sampling

“…Furthermore, calibration estimation is another common statistical approach that relies on the use of auxiliary information to adjust the original weights of the design and improve the accuracy of estimators. The authors of [20] were pioneers in the use of calibration estimation with survey data and several additional works on mean estimation have been published since (for example, see [21][22][23]).…”