Proposed Calibration Estimator Research Articles

A new modified estimator of population variance in calibrated survey sampling

In survey statistics, estimating and reducing population variation is crucial. These variations can occur in any sampling design, including stratified random sampling, where stratum weights may increase the variance of estimators. Calibration techniques, which use additional auxiliary information, can help mitigate this issue. This paper examines three calibration-based estimators—calibration variance, calibration ratio, and calibration exponential ratio estimators—within the framework of stratified random sampling. The study generates data from normal, gamma, and exponential distributions to test these estimators. Results demonstrate that the proposed calibration estimators offer more accurate estimates of population variance and outperform existing methods in estimating population variance under stratified random sampling, providing more accurate and reliable estimates.

Treating the problem of non-response in stratified random sampling under calibration approach

In the present study, we suggested a chi-square-type distance function that works well for non-response situations and we have derived a new calibration-based estimator using such a kind of distance function, which is used to estimate the mean of a stratified population. The proposed estimator is derived through the implementation of a reweighting technique referred to as the calibration approach, aimed at improving upon Hansen and Hurwitz’s (1946) estimator. Typically, in situations where some units do not respond, researchers adjust the stratum weights to obtain an estimator for the mean of a stratified population using the calibration approach. In this study, the weights given to the responding units in the sample and the units in the sub-sample taken from the non-responding sample were calibrated to derive the calibration estimator. We assume that the unit non-response problem impacts both study and auxiliary variables. To examine the performance of the proposed calibration estimator in scenarios involving non-response, we have carried out empirical studies.

Evaluation of the synthetic estimators with non-respondent for small domain

The present work gives generalized form of the class of estimators if unit non-response is acquired in small domains. We have obtained indirect method like synthetic. It has provided specific instances where the proposed estimators are unbiased. It has also given a generalized form of the synthetic estimators. The four estimators were investigated with coefficient of variation and kurtosis constants. Because, these are obtained from the available variable. We conducted atheoretical comparison between traditional and proposed calibration estimators for estimating the domain totals. It found that the proposed estimators are more efficient than traditional estimators for investigate small domains.

Calibration estimator for a sensitive variable using dual auxiliary information under measurement errors

In survey research, it is commonly assumed that all the observations are measured accurately. However, in practice, this assumption is not achieved due to many reasons, so it causes measurement errors to be inevitably present in the sample estimation. This article addresses the problem of estimation of finite population mean under stratified random sampling in the presence of measurement errors. A calibration estimator is proposed for the sensitive variable by utilizing suitable calibration techniques, which can be applied to obtain the optimal strata weight. The calibration estimator not only incorporates the auxiliary information but also the ranks of the auxiliary variable. Expressions for bias and mean square error are derived up to first order of approximation. Simulation studies and real-life datasets are used to assess the performances of the proposed estimator by comparing them with the contemporary estimators in the presence and absence of measurement errors. The theoretical and empirical studies demonstrate that the proposed calibration estimator consistently outperforms classical mean, usual ratio, conventional difference, Khail randomized response estimators.

Calibration Estimation of Population Proportion in Probability Proportional to Size Sampling in the Presence of Non-Response

Objectives: In this article, we addressed the problem of estimation of the finite population proportion under the Probability Proportional to Size (PPS) sampling technique, when the complete information is unavailable due to the presence of non-response. We developed calibrated estimators of the population proportion under PPS sampling in the presence of nonresponse based on the availability of auxiliary information. Methods: The expressions for the mean squared errors of the suggested estimators were developed to the first order of approximation. The developed estimators of the population proportion are compared with the design-based Horvitz-Thompson estimator and Horvitz-Thompson type calibration estimator which were obtained on the complete response units along with the design-based Hansen and Hurwitz type estimator in the presence of non-response. A Simulation study has also been conducted to support the performance of the developed estimators of population proportion with the help of two real datasets, by computing Percentage Absolute Relative Bias (%ARB) and Percentage Relative Root Mean Squared Error (%RRMSE) using R software. Findings: The simulation study supported the performance of the developed estimators of the finite population proportion based on %ARB and %RRMSE. The proposed calibration estimators of population proportion are more efficient than the other considered estimators in the presence of non-response. Novelty: The proposed new calibrated estimators have practical implications in the estimation of finite population proportions. Keywords: Auxiliary information, Calibration Approach, Non­response, Population proportion, PPS sampling

A calibration-based approach on estimation of mean of a stratified population in the presence of non response

In this article, we have derived a new calibration estimator of the population mean in the stratified random sampling under the presence of non response. The proposed calibration estimator has been obtained by making some improvements in the Hansen and Hurwitz (1946) estimator. For this purpose, we have gainfully utilized the information on a single auxiliary variable to obtain a set of new calibrated weights that increase the precision of the estimates. The proposed calibration estimator has been derived using the chi-square type distance function subject to some calibration constraints based on the auxiliary information. The Taylor linearization technique has been used to derive the expression for the variance of the proposed calibration estimator. We have also performed an empirical study based on the hypothetically generated data and real data to study the performance of the proposed calibration estimator. The proposed calibration estimator has been found more efficient than the usual Hansen and Hurwitz (1946) estimator and the recent calibration estimator proposed by Dykes et al. (2015).

Separate Ratio Estimator Using Calibration Approach for the Population mean in Stratified Random Sampling

In this paper we investigate the problem of estimation of finite population mean using auxiliary information. The aim of this paper is to modify a separate ratio estimator by using calibration approach for the population mean using stratified random sampling. We use the calibration approach to improve the precision of estimate of the population parameter by incorporating auxiliary information. We use the chi-square distance function to minimize the distance between the original design weight and the new design weight. We use two constraints called calibration equations to find the new calibration weights. We use the Taylor’s linearization technique to find the approximate mean square (MSE) of the proposed estimator up to the first degree of approximation. We conduct a simulation study to assess the efficiency of the proposed calibration estimator based on an artificially generated data set. An empirical study has also been conducted to judge the merits of the proposed estimator, which shows that the proposed estimator performs better than the proposed estimator [9] and the usual separate ratio estimator.

Calibration estimator of population mean under stratified two-phase sampling using two auxiliary variables

In the present paper, we have tried to discover a new calibration estimator of the population mean under stratified two-phase sampling design utilizing the information on two auxiliary variables. In order to develop the calibration estimator, we have obtained new optimum stratum weights so that the MSE/Variance of the estimator would be minimized. Moreover, we have compared the efficiency of the proposed calibration estimator with that of the calibration estimator considered under the stratified two-phase sampling scheme using single auxiliary variable. An empirical illustration along with a simulation analysis has also been presented to demonstrate the theoretical results.

New improved calibration estimator based on two auxiliary variables in stratified two-phase sampling

This paper considers the problem of estimating the population mean of the study variable when auxiliary information is not available and proposes new calibration approach alternative to the recent existing calibration estimators for estimating population mean of the study variable using two auxiliary variables in stratified two-phase sampling. The theory of new calibration estimation is given and optimum weights are derived under two-phase sampling approach. A simulation study is carried out to performance of the proposed calibration estimator with other existing calibration estimators. The results demonstrate that the proposed calibration estimator is more efficient than other existing calibration estimators of the population mean in stratified two-phase sampling.

Treating nonresponse in the estimation of the distribution function

The estimation of a finite population distribution function is considered when there are missing data. Calibration adjustment is used for dealing with nonresponse at the estimation stage. Several procedures are proposed and compared. A numerical study is carried out to evaluate the performances of estimators. Computational problems with the implementation of the proposed calibration estimators are also considered.

Some calibration estimators for finite population mean in two-stage stratified random sampling

In the present article, an effort has been made to develop calibration estimators of the population mean under two-stage stratified random sampling design when auxiliary information is available at primary stage unit (psu) level. The properties of the developed estimators are derived in-terms of design based approximate variance and approximate consistent design based estimator of the variance. Some simulation studies have been conducted to investigate the relative performance of calibration estimator over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. Proposed calibration estimators have outperformed the usual estimator without using auxiliary information.

New calibration estimator in stratified sampling

ABSTRACTThis paper develops the theory of calibration estimation and proposes calibration approach alternative to existing calibration estimators for estimating population mean of the study variable using auxiliary variable in stratified sampling. The theory of new calibration estimation is given and optimum weights are derived. A simulation study is carried out to performance of the proposed calibration estimator with other existing calibration estimators. The results reveal that the proposed calibration estimators are more efficient than Tracy et al., Singh et al., Singh calibration estimators of the population mean.

New calibration estimator based on two auxiliary variables in stratified sampling

ABSTRACTIn recent years, calibration estimation has become an important field of research in survey sampling. This paper proposes a new calibration estimator for the population mean in the presence of two auxiliary variables in stratified sampling. The theory of new calibration estimator is given and optimum calibration weights are derived. A simulation study is carried out to performance of the proposed calibration estimator over other existing calibration estimators. The results reveal that the proposed calibration estimators are more efficient than other existing calibration estimators in stratified sampling.

A note on calibration weightings for stratified double sampling with equal probability

ABSTRACTThis study proposes a more efficient calibration estimator for estimating population mean in stratified double sampling using new calibration weights. The variance of the proposed calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed calibration estimator and existing calibration estimators in stratified double sampling. Analytical results showed that the proposed calibration estimator is more efficient than existing members of its class in stratified double sampling. Analysis and evaluation are presented.

District-Level Crop Yield Estimation Using Calibration Approach

Estimation of major crop yield rates at the district level using calibration estimation technique is reported here when auxiliary information is available at the unit level only for the selected villages within each district and when the sampling design under consideration is two-stage equal probability without replacement. An estimator was developed for the complex sampling design under consideration using the calibration approach. Through evaluation using real data collected from a pilot survey, we found that the proposed calibration estimator performs better than the usual design-based Horvitz-Thompson estimator under two-stage sampling design.

Calibration approach estimation of the mean in stratified sampling and stratified double sampling

ABSTRACTCalibration estimation improves the precision of the estimates of population parameters by incorporating specified auxiliary information. A class of calibration estimators has been proposed for estimating the population mean by making use of a set of calibration constraints in stratified sampling. The estimator of variance of the proposed calibration estimator of the mean is derived using a lower level calibration approach. The idea is extended for stratified double sampling. A simulation study is used to evaluate the performances of the proposed estimators by comparing them with the similar estimators developed by Tracy, Singh and Arnab (2003) based on different sets of calibration constraints.

Estimating Population Proportions by Means of Calibration Estimators

This paper considers the problem of estimating the population proportion of a categorical variable using the calibration framework. Different situations are explored according to the level of auxiliary information available and the theoretical properties are investigated. A new class of estimator based upon the proposed calibration estimators is also defined, and the optimal estimator in the class, in the sense of minimal variance, is derived. Finally, an estimator of the population proportion, under new calibration conditions, is defined. Simulation studies are considered to evaluate the performance of the proposed calibration estimators via the empirical relative bias and the empirical relative efficiency, and favourable results are achieved.

Calibration Estimation in Survey Sampling

Summary Calibration estimation, where the sampling weights are adjusted to make certain estimators match known population totals, is commonly used in survey sampling. The generalized regression estimator is an example of a calibration estimator. Given the functional form of the calibration adjustment term, we establish the asymptotic equivalence between the functional‐form calibration estimator and an instrumental variable calibration estimator where the instrumental variable is directly determined from the functional form in the calibration equation. Variance estimation based on linearization is discussed and applied to some recently proposed calibration estimators. The results are extended to the estimator that is a solution to the calibrated estimating equation. Results from a limited simulation study are presented.

The Calibration for Stratified Randomized Response Estimators

In this paper, we propose the calibration procedure for the valiance reduction of the stratified Warner's randomized response estimators, which suggested by Hong et al. (1994) and Kim and Warde (2004), using auxiliary information at the population level. It is shown that the proposed calibration estimators are more efficient than the ordinary Warner's estimators.

Optimal calibration estimators in survey sampling

We show that the model-calibration estimator for the finite population mean, which was proposed by Wu & Sitter (2001) through an intuitive argument, is optimal among a class of calibration estimators. We also present optimal calibration estimators for the finite population distribution function, the population variance, the variance of a linear estimator and other quadratic finite population functions under a unified framework. The proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified. A limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial. The question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology. Some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation.