ESTIMATION OF POPULATION MEAN USING AUXILIARY INFORMATION IN PRESENCE OF MEASUREMENT ERRORS (original) (raw)

The Influence of Measurement Errors on Generalized Estimator of Population Mean

Asian Journal of Probability and Statistics, 2022

This paper proposed a generalized estimator of population mean in the presence of correlated and uncorrelated measurement errors under simple random strategy. Some known estimators belong to this class of proposed estimator. Under the large sample approximation, the properties of the proposed estimator namely bias and mean squared error were obtained. Theoretical comparison was carried out on the members of the proposed class of estimators when measurement errors are correlated and when they are uncorrelated and the necessary conditions under which the proposed estimator at its optimum value is expected to be more efficient than the existing estimators of finite population mean were obtained. It was observed that correlated and uncorrelated measurement errors inflate the bias and mean squared error of the proposed estimator. The paper concluded that the proposed estimator is more efficient than usual unbiased estimator and some members of the class of proposed estimator.

IMPROVED ESTIMATION OF FINITE POPULATION VARIANCE USING AUXILIARY INFORMATION IN PRESENCE OF MEASUREMENT ERRORS

This paper discusses the problem of estimating the finite population variance using auxiliary information in presence of measurement errors. We have suggested a class of estimators and its properties are studied under large sample approximation. It has been shown that the usual unbiased estimator and the estimators due to Sharma and Singh [A generalized class of estimators for finite population variance in presence of measurement errors, Journal of Modern Applied Statistical Methods, (2013), 12(2), 231-241.] are members of the proposed class of estimators. An alternative expression of the mean squared error of one the estimator due to Sharma and Singh [A generalized class of estimators for finite population variance in presence of measurement errors, Journal of Modern Applied Statistical Methods, (2013), 12(2), 231-241.

Estimating Population Mean using Known Coefficient of Variation under Measurement Errors

The present paper deals with the effects of measurement errors on a regression-type estimator for estimating population mean using known coefficient of variation. The proposed estimator has made the use of auxiliary information to improve efficiency under the assumption that measurement error is present both in study and auxiliary variable. The bias and mean square error of proposed estimator are found. A comparative study with mean per unit estimator under measurement errors has also been made. Theoretical conclusions are verified by the empirical study.

An Estimator for Mean Estimation in Presence of Measurement Error

In sample survey, we estimate of population parameter on the basis of collected data. It may originate from various kinds of sampling methods such as simple random sampling, stratified sampling, systematic sampling etc. Various methods of estimation are used under the assumption that observations collected are true (error free). In real life this kind of situations are not tenable. The real data contains observational error due to many reasons like memory failure, over-reporting, under-reporting, prestige bias etc (See fig. 1.0). These are also called measurement error. [1, 12]. Assume that an agency is conducting a survey of army solders to know income and expenditure pattern. Since income is a subject of high privacy and sensitivity, the surveyor ABSTRACT In sample surveys, while data collection the information reported by respondents are often underreported or over-reported. For example, age is usually under-reported and income usually over-reported in the individual information of working group. Because of this, the survey results are affected by error called measurement error. Most of the part of sampling theory is based on assumption that data over variable under study are available correctly (or truly). But in field practice, it often violates and existing methodologies of parameter estimation are not capance to cope with. This paper presents a new technique of mean estimation in presence of measurement error in sample survey. An estimator is proposed and its properties are discussed with expression based comparative study.

Some Improved Estimators for Estimating Population Variance in the Presence of Measurement Errors

In this paper the problem of estimating finite population variance under measurement errors is discussed. Some estimators based on arithmetic mean, geometric mean and harmonic mean under measurement errors are proposed. Biases and mean square errors of proposed estimators are calculated to the first order of approximation. A comparative study is made among the usual unbiased estimator, usual ratio estimator and Kadilar and Cingi(2006a) estimator. Hypothetical study is also given at the end of the paper to support the theoretical findings.

An Efficient Estimator for Estimating Population Variance in Presence of Measurement Errors

The present paper advocates the problem of estimating population variance when the measurement errors are present in both the study variable and the auxiliary variable.Bias and Mean Square Error (MSE) of the proposed estimator is obtained up to first order of approximation. Theoretical efficiency comparison between usual variance estimator and the proposed estimator is also made under measurement errors.Theoretical results are supported by simulation study using R software.