On Using the Conventional and Nonconventional Measures of the Auxiliary Variable for Mean Estimation

In this paper, we propose an improved new class of exponential-ratio-type estimators for estimating the finite population mean using the conventional and the nonconventional measures of the auxiliary variable. Expressions for the bias and MSE are obtained under large sample approximation. Both simulation and numerical studies are conducted to validate the theoretical findings. Use of the conventional and the nonconventional measures of the auxiliary variable is very common in survey research, but we observe that this does not add much value in many of the estimators except for our proposed class of estimators.

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A family of estimators of population mean using multi-auxiliary variate and post-stratification

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2010.15.2.14356 ◽

2010 ◽

Vol 15 (2) ◽

pp. 233-253 ◽

Cited By ~ 5

Author(s):

Gajendra K. Vishwakarma ◽

Housila P. Singh ◽

Sarjinder Singh

Keyword(s):

Empirical Study ◽

Stratified Sampling ◽

Large Sample ◽

Population Mean ◽

Auxiliary Variate ◽

Large Sample Approximation ◽

Sample Approximation ◽

Optimum Estimator ◽

Class Of Estimators ◽

Approximate Variance

This paper suggests a family of estimators of population mean using multiauxiliary variate based on post-stratified sampling and its properties are studied under large sample approximation. Asymptotically optimum estimator in the class is identified alongwith its approximate variance formulae. The proposed class of estimators is also compared with corresponding unstratified class of estimators based on estimated optimum value. At the end, an empirical study has been carried out to support the proposed methodology.

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Finite Population Mean Estimation through a Two-Parameter Ratio Estimator Using Auxiliary Information in Presence of Non-Response

Journal of Applied Mathematics Statistics and Informatics ◽

10.1515/jamsi-2016-0006 ◽

2016 ◽

Vol 12 (2) ◽

pp. 5-39 ◽

Cited By ~ 1

Author(s):

S. K. Pal ◽

H. P. Singh

Keyword(s):

Auxiliary Information ◽

Auxiliary Variable ◽

Human Populations ◽

Ratio Estimator ◽

Population Mean ◽

Parameter Ratio ◽

Mean Estimation ◽

Large Sample Approximation ◽

Respondent Group ◽

Sample Approximation

Abstract In surveys covering human populations it is observed that information in most cases are not obtained at the first attempt even after some callbacks. Such problems come under the category of non-response. Surveys suffer with non-response in various ways. It depends on the nature of required information, either surveys is concerned with general or sensitive issues of a society. Hansen and Hurwitz (1946) have considered the problem of non-response while estimating the population mean by taking a subsample from the non-respondent group with the help of extra efforts and an estimator was suggested by combining the information available from the response and nonresponse groups. We also mention that in survey sampling auxiliary information is commonly used to improve the performance of an estimator of a quantity of interest. For estimating the population mean using auxiliary information in presence of non-response has been discussed by various authors. In this paper, we have developed estimators for estimating the population mean of the variable under interest when there is non-response error in the study as well as in the auxiliary variable. We have studied properties of the suggested estimators under large sample approximation. Comparison of the suggested estimators with usual unbiased estimator reported by Hansen and Hurwitz (1946) and the ratio estimator due to Rao (1986) have been made. The results obtained are illustrated with aid of an empirical study.

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Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme

Journal of Applied Mathematics Statistics and Informatics ◽

10.2478/jamsi-2020-0005 ◽

2020 ◽

Vol 16 (1) ◽

pp. 61-75

Author(s):

S. Baghel ◽

S. K. Yadav

Keyword(s):

Random Sampling ◽

Simple Random Sampling ◽

Auxiliary Variable ◽

Sampling Scheme ◽

Order Of Approximation ◽

Study Variable ◽

Population Mean ◽

First Order ◽

New Class ◽

Class Of Estimators

AbstractThe present paper provides a remedy for improved estimation of population mean of a study variable, using the information related to an auxiliary variable in the situations under Simple Random Sampling Scheme. We suggest a new class of estimators of population mean and the Bias and MSE of the class are derived upto the first order of approximation. The least value of the MSE for the suggested class of estimators is also obtained for the optimum value of the characterizing scaler. The MSE has also been compared with the considered existing competing estimators both theoretically and empirically. The theoretical conditions for the increased efficiency of the proposed class, compared to the competing estimators, is verified using a natural population.

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Two- Phase Stratified Sampling Estimator for Population Mean in The Presence of Nonresponse Using Single Auxiliary Variable

Mathematical Journal of Interdisciplinary Sciences ◽

10.15415/mjis.2020.82006 ◽

2020 ◽

Vol 8 (2) ◽

pp. 49-56

Author(s):

Akan Anieting

Keyword(s):

Mean Squared Error ◽

Auxiliary Variable ◽

Stratified Sampling ◽

Second Phase ◽

Two Phase ◽

Population Mean ◽

Squared Error ◽

Large Sample Approximation ◽

Sample Approximation ◽

Phase Sample

In this article, a new estimator for population mean in two-phase stratified sampling in the presence of nonresponse using single auxiliary variable has been proposed. The bias and Mean Squared Error (MSE) of the proposed estimator has been given using large sample approximation. The empirical study shows that the MSE of the proposed estimator is more efficient than existing estimators. The optimum values of first and second phase sample have been determined.

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Some Median Type Estimators to Estimate the Finite Population Mean

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2020/v7i430192 ◽

2020 ◽

pp. 48-58

Author(s):

Waqar Hafeez ◽

Javid Shabbir ◽

Muhammad Taqi Shah ◽

Shakeel Ahmed

Keyword(s):

Linear Regression ◽

Finite Population ◽

Auxiliary Variable ◽

Maximum Efficiency ◽

Order Of Approximation ◽

Study Variable ◽

Sample Mean ◽

First Order ◽

Regression Estimators ◽

Class Of Estimators

Researchers always appreciates estimators of finite population quantities, especially mean, with maximum efficiency for reaching to valid statistical inference. Apart from ratio, product and regression estimators, exponential estimators are widely considered by survey statisticians. Motivated from the idea of exponential type estimators, in this article, we propose some new estimators utilizing known median of the study variable with mean of auxiliary variable. Theoretical properties of the suggested estimators are studied up to first order of approximation. In addition, an empirical and simulation study the comparison of median based proposed class of estimators with sample mean, ratio and linear regression estimators are discussed. The results expose that the proposed estimators are more efficient than the existing estimators.

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A New Exponential Approach for Reducing the Mean Squared Errors of the Estimators of Population Mean Using Conventional and Non-Conventional Location Parameters

Journal of Modern Applied Statistical Methods ◽

10.22237/jmasm/1568246400 ◽

2020 ◽

Vol 18 (1) ◽

Author(s):

Housila P. Singh ◽

Anita Yadav

Keyword(s):

Large Sample ◽

Population Mean ◽

Mean Squared Errors ◽

Large Sample Approximation ◽

Location Parameters ◽

Sample Approximation ◽

The Mean

Classes of ratio-type estimators t (say) and ratio-type exponential estimators te (say) of the population mean are proposed, and their biases and mean squared errors under large sample approximation are presented. It is the class of ratio-type exponential estimators te provides estimators more efficient than the ratio-type estimators.

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