scholarly journals A Family of Difference-Cum-Exponential Type Estimators for Estimating the Population Variance Using Auxiliary Information in Sample Surveys

2014 ◽  
Vol 1 ◽  
pp. 15-21
Author(s):  
H.S. Jhajj ◽  
Kusam Lata
Keyword(s):  
Linear Regression ◽  
Exponential Type ◽  
Random Sampling ◽  
Sampling Design ◽  
Mean Squared Error ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Double Sampling ◽  
Population Variance ◽  
Squared Error

Using auxiliary information, a family of difference-cum-exponential type estimators for estimating the population variance of variable under study have been proposed under double sampling design. Expressions for bias, mean squared error and its minimum values have been obtained. The comparisons have been made with the regression-type estimator by using simple random sampling at both occasions in double sampling design. It has also been shown that better estimators can be obtained from the proposed family of estimators which are more efficient than the linear regression type estimator. Results have also been illustrated numerically as well asgraphically.

scholarly journals A generalized exponential-type estimator for population mean using auxiliary attributes

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0246947
Author(s):  
Sohail Ahmad ◽  
Muhammad Arslan ◽  
Aamna Khan ◽  
Javid Shabbir
Keyword(s):  
Exponential Type ◽  
Random Sampling ◽  
Finite Population ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Stratified Random Sampling ◽  
Population Mean ◽  
First Order ◽  
Squared Error ◽  
Class Of Estimators

In this paper, we propose a generalized class of exponential type estimators for estimating the finite population mean using two auxiliary attributes under simple random sampling and stratified random sampling. The bias and mean squared error (MSE) of the proposed class of estimators are derived up to first order of approximation. Both empirical study and theoretical comparisons are discussed. Four populations are used to support the theoretical findings. It is observed that the proposed class of estimators perform better as compared to all other considered estimator in simple and stratified random sampling.

scholarly journals ESTIMATION OF POPULATION VARIANCE IN LOG – PRODUCT TYPE ESTIMATORS UNDER DOUBLE SAMPLING SCHEME

2019 ◽  
pp. 11-20
Author(s):  
Prabhakar Mishra ◽  
Rajesh Singh ◽  
Supriya Khare
Keyword(s):  
Random Sampling ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Product Type ◽  
Sampling Scheme ◽  
Double Sampling ◽  
Population Variance ◽  
Population Mean ◽  
Ancillary Information

It is experienced that auxiliary information when suitably incorporated yields more efficient and precise estimates. Mishra et al. (2017) have introduced a log type estimator for estimating unknown population mean using ancillary information in simple random sampling. Here we propose an improved log-product type estimator for population variance under double sampling. Properties of the estimators are studied both mathematically and numerically.  

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 Sampling in Difficult Settings: A Simulation Study Comparing Several Sampling Methods

2020 ◽  
Author(s):  
Harry Shannon ◽  
Patrick D. Emond ◽  
Benjamin M. Bolker ◽  
Román Viveros-Aguilera
Keyword(s):  
Random Sampling ◽  
Sampling Methods ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Target Population ◽  
Original Method ◽  
World Health ◽  
Root Mean Squared Error ◽  
Relative Risks ◽  
Squared Error

Abstract Background: Taking a representative sample to determine prevalence of variables like disease is difficult when little is known about the target population. Several methods have been proposed, including a recent revision of the World Health Organization’s Extended Program on Immunization (EPI) surveys. The original method uses probability proportional to size to sample towns and a nearest neighbour approach to sampling households within towns. The new version samples from relatively small areas and conducts a probability sample of households within those areas. Other techniques sample within towns from circles around randomly identified points (‘Circles’) or from randomly sampled squares in a superimposed grid (‘Square’). We compared these sampling methods in multiple virtual populations using computer simulation.Methods: We constructed 50 virtual populations with varying characteristics. Populations comprised about a million people across 300 towns. We created three more populations with different prevalences of disease but with uniform characteristics across each population. We created a binary exposure variable and allocated disease statuses to individuals assuming different Relative Risks of exposure. We simulated thirteen methods of sampling: simple random sampling; the original EPI method and variants; the Square and Circle methods; and the new EPI method. For each population, each sampling method, and each of three sample sizes per cluster (7, 15, and 30), we simulated 1,000 samples. For most sampling methods, the clusters were towns. We conducted simulations using the same 30 clusters and using a freshly-chosen set of clusters. For each simulation we estimated prevalence and RRs and computed the Root Mean Squared Error for the 1,000 samples.Results: The Circle and Square methods produced almost identical results, so we report only the Square method results. The Root Mean Squared Error for the Square method was almost universally best relative to simple random sampling for estimating prevalence, and generally best when estimating Relative Risks. The revised EPI approach was less good, but generally better than the original EPI. Conclusions: The Square method is recommended as statistically optimal, unless practical considerations favour another approach.

scholarly journals ln-Type Variance Estimators in Simple Random Sampling

2020 ◽  
pp. 689-696
Author(s):  
Hatice Oncel Cekim ◽  
Cem Kadilar
Keyword(s):  
Exponential Type ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
The Other ◽  
Data Sets ◽  
Population Variance ◽  
Sampling Studies ◽  
Variance Estimators ◽  
Study Support ◽  
First Time

Until now, various types of estimators have been used for estimating the population variance in simple random sampling studies, including ratio, product, regression and exponential-type estimators. In this article, we propose a family of -type estimators for the first time in the simple random sampling and show that they are more efficient than the other types of estimators under certain conditions obtained theoretically. Numerical illustrations and a simulation study support our findings in theory. In addition, it has been shown how to determine the optimal points in order to reach the minimum MSE values with the properties of the ln-type estimators in the different data sets.

scholarly journals Estimation of a total for rotated sample design using auxiliary information

2009 ◽  
Vol 50 ◽  
Author(s):  
Viktoras Chadyšas
Keyword(s):  
Random Sampling ◽  
Sampling Design ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Sampling Procedure ◽  
Sample Design ◽  
Successive Sampling ◽  
Phase Sampling ◽  
Approximate Variance ◽  
Multi Phase

In this paper we focus on constructions of the total estimator for rotated sampling design. Successive sampling procedure using multi-phase sampling design have been developed. The composite ratio type estimator of the total using auxiliary  information and its approximate variance is constructed under simple random sampling design on each phase.

scholarly journals Estimation of employed persons in the case of sample rotation

2008 ◽  
Vol 48 ◽  
Author(s):  
Viktoras Chadyšas ◽  
Danutė Krapavickaitė
Keyword(s):  
Random Sampling ◽  
Sampling Design ◽  
Labour Force ◽  
Auxiliary Information ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ratio Estimator ◽  
Labour Force Survey ◽  
The Real ◽  
Sample Rotation

The aim of the paper – to investigate effectiveness of the ratio estimator in the labour force survey in the case of the simple random sampling with rotation. For each quarter of the year one fourth of the previousquarter sample is changed with the new one, and three fourth’s are remaining the same. After simplification of the sampling design the estimator using auxiliary information and its approximate variance is constructed. The accuracy of the estimator obtained is studied by modelling with the real data.

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