scholarly journals Use of Auxiliary Variables and Asymptotically Optimum Estimators in Double Sampling

2016 ◽  
Vol 5 (3) ◽  
pp. 55 ◽  
Author(s):  
M. E. Kanwai ◽  
O. E. Asiribo ◽  
A. Isah
Keyword(s):  
Mean Squared Error ◽  
Population Level ◽  
Auxiliary Variable ◽  
Sample Survey ◽  
Comparative Approach ◽  
Double Sampling ◽  
Auxiliary Variables ◽  
Two Phase ◽  
Optimum Estimator ◽  
The Mean

This paper explore the need for exploiting auxiliary variables in sample survey and utilizing asymptotically optimum estimator in double sampling to increase the efficiency of estimators. The study proposed two types of estimators with two auxiliary variables for two phase sampling when there is no information about auxiliary variables at population level. The expressions for the Mean Squared Error (MSE) of the proposed estimators were derived to the first order of approximation. An empirical comparative approach of the minimum variances and percent relative efficiency were adopted to study the efficiency of the proposed and existing estimators. It was established that, the proposed estimators performed more efficiently than the mean per unit estimator and other previous estimators that don’t use auxiliary variable and that are not asymptotically optimum. Also, it was established that estimators that are asymptotically optimum that utilized single auxiliary variable are more efficient than those that are not asymptotically optimum with two auxiliary variables.

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals Some Improved Estimators in Double Sampling Using two Auxiliary Variables

2015 ◽  
Vol 19 (2) ◽  
pp. 97
Author(s):  
Mohammad S. Ahmed
Keyword(s):  
Mean Squared Error ◽  
Double Sampling ◽  
Auxiliary Variables ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Series Expression ◽  
Optimum Estimator ◽  
Class Of Estimators ◽  
Improved Estimators ◽  
Taylor’S Series

Dash and Mishra [1] suggested an improved class of estimators without defining the optimum estimator. However, they gave the wrong Taylor’s series expression of their class of estimator and their minimum mean squared error expressions are also incorrect. Here we show that Ahmed et al.’s [2] class of chain estimators is more efficient than Dash and Mishra’s [1], with minimum mean squared error.  

Ratio-Type Estimation Using Scrabled Auxiliary Variables in Stratification Under Simple Random Sampling and Ranked Set Sampling

2022 ◽  
pp. 62-85
Author(s):  
Carlos N. Bouza-Herrera ◽  
Jose M. Sautto ◽  
Khalid Ul Islam Rather
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Auxiliary Variables ◽  
Mild Conditions ◽  
Squared Error ◽  
The Mean ◽  
Better Than

This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.

scholarly journals On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Saddam Hussain ◽  
Mi Zichuan ◽  
Sardar Hussain ◽  
Anum Iftikhar ◽  
Muhammad Asif ◽  
...  
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Distribution Functions ◽  
Supplementary Information ◽  
Auxiliary Variables ◽  
Estimation Of Distribution

In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.

scholarly journals A Study on the Chain Ratio-Type Estimator of Finite Population Variance

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yunusa Olufadi ◽  
Cem Kadilar
Keyword(s):  
Finite Population ◽  
Numerical Comparison ◽  
Mean Square ◽  
Auxiliary Variables ◽  
Population Variance ◽  
Two Phase ◽  
First Order ◽  
Phase Sampling ◽  
The Mean ◽  
Two Phase Sampling

We suggest an estimator using two auxiliary variables for the estimation of the unknown population variance. The bias and the mean square error of the proposed estimator are obtained to the first order of approximations. In addition, the problem is extended to two-phase sampling scheme. After theoretical comparisons, as an illustration, a numerical comparison is carried out to examine the performance of the suggested estimator with several estimators.

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

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.

Multi-phase sampling

2019 ◽  
pp. 200-218
Author(s):  
David G. Hankin ◽  
Michael S. Mohr ◽  
Ken B. Newman
Keyword(s):  
Optimal Allocation ◽  
Cost Effective ◽  
Auxiliary Variable ◽  
Sampling Effort ◽  
Second Phase ◽  
Two Phase ◽  
Phase Errors ◽  
The Mean ◽  
Phase Sample ◽  
Multi Phase

Attention is restricted to two-phase or double sampling. A large first-phase sample is used to generate a very good estimate of the mean or total of an auxiliary variable, x, which is relatively cheap to measure. Then, a second-phase sample is selected, usually from the first-phase sample, and both auxiliary and target variables are measured in selected second-phase population units. Two-phase ratio or regression estimators can be used effectively in this context. Errors of estimation reflect first-phase uncertainty in the mean or total of the auxiliary variable, and second-phase errors reflect the nature of the relation and correlation between auxiliary and target variables. Accuracy of the two-phase estimator of a proportion depends on sensitivity and specificity. Sensitivity is the probability that a unit possessing a trait (y = 1) will be correctly classified as such whenever the auxiliary variable, x, has value 1, whereas specificity is the probability that a unit not possessing a trait (y = 0) will be correctly classified as such whenever the auxiliary variable, x, has value 0. Optimal allocation results for estimation of means, totals, and proportions allow the most cost-effective allocation of total sampling effort to the first- and second-phases. In double sampling with stratification, a large first-phase sample estimates stratum weights, a second-phase sample estimates stratum means, and a stratified estimator gives an estimate of the overall population mean or total.

scholarly journals Small Area Estimation under Spatial Multivariate Fay–Herriot Model

2021 ◽  
Author(s):  
hukum chandra ◽  
Saurav Guha
Keyword(s):  
Small Area ◽  
Mean Squared Error ◽  
National Sample ◽  
Sample Survey ◽  
Consumer Expenditure ◽  
Squared Error ◽  
Food And Nutrition ◽  
Empirical Performance ◽  
Nutrition Intake ◽  
The Mean

Spatial version of multivariate Fay–Herriot model is introduced and small area predictor under this model is proposed. The mean squared error (MSE) estimation of the proposed small area predictor is also developed. The empirical performance of the proposed small area predictor and the MSE estimator are evaluated through simulation studies. The empirical results clearly show that the proposed small area predictor outperforms the existing predictors. The proposed MSE estimator tracks the actual value of MSE reasonably well with acceptable coverage rate. An application to estimate the disparities in food and nutrition intake from the 2011–12 Household Consumer Expenditure Survey data collected by the national sample survey office of India is also presented.

scholarly journals Modified Regression Type Estimators in the Presence of Non-Response in Two Phase sampling

2018 ◽  
Vol 6 (07) ◽  
Author(s):  
John Kung’u Wanjiru ◽  
Grace Chumba
Keyword(s):  
Single Phase ◽  
Complete Response ◽  
Auxiliary Variable ◽  
Degree Of Approximation ◽  
Sample Survey ◽  
Sampling Scheme ◽  
Two Phase ◽  
Population Mean ◽  
Phase Sampling ◽  
Two Phase Sampling

It is a common experience in sample survey that data cannot always be collected for all units selected in the sample at the first attempt and even after some call-backs. An estimate obtained from such incomplete data may be misleading because of the non-response in the data. In addition, the population mean of the auxiliary variable from the previous census may not be available. In this paper, Modified regression type estimators proposed by Tum et al. (2014) in single phase sampling, assuming complete response, have been proposed to estimate the population mean of the study variable in the presence of non-response under two phase sampling scheme. The expression of mean squared errors (MSE) based on the proposed estimators have been derived under two phase sampling to the first degree of approximation. A comparison of the proposed estimators with the usual unbiased estimator and existing estimators under two phase sampling scheme have been carried out. The proposed Modified regression type estimators have been found to be the most efficient compared to the existing estimators and they are recommended for use in practice.

scholarly journals Development of Efficient Estimation Technique for Population Mean in Two Phase Sampling Using Fuzzy Tools

2017 ◽  
Vol 13 (2) ◽  
pp. 5-28 ◽  
Author(s):  
P. Parichha ◽  
K. Basu ◽  
A. Bandyopadhyay ◽  
P. Mukhopadhyay
Keyword(s):  
Natural Population ◽  
Efficient Estimation ◽  
Double Sampling ◽  
Estimation Technique ◽  
Auxiliary Variables ◽  
Two Phase ◽  
Data Set ◽  
Population Mean ◽  
Phase Sampling ◽  
Two Phase Sampling

Abstract The present investigation deals with the problem of estimation of population mean in two-phase (double) sampling. Utilizing information on two auxiliary variables, one chain exponential ratio and regression type estimator has been proposed and its properties are studied under two different structures of twophase sampling. To make the estimator practicable, unbiased version of the proposed strategy has also been developed. The dominance of the suggested estimator over some contemporary estimators of population mean has been established through numerical illustrations carried over the data set of some natural population and artificially generated population. Categorization of the dominance ranges of the proposed estimation strategies are deployed through defuzzification tools, which are followed by suitable recommendations.

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