scholarly journals New Stratified Bayesian Estimators Using Warner’s Randomized Response Technique Through Mixed Priors

2018 ◽  
Vol 10 (3) ◽  
pp. 249-259
Author(s):  
A. O. Adepetun ◽  
A. A. Adewara
Keyword(s):  
Random Sampling ◽  
Prior Information ◽  
Mean Squared Error ◽  
Performance Criteria ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Squared Error ◽  
Absolute Bias ◽  
Alternative Beta ◽  
Bayesian Estimators

In this paper, we propose new stratified Bayesian estimators of population proportion of a sensitive trait by adopting a mixture of alternative beta distributions as quantification of prior information in a stratified random sampling situation. Data were collected through Warner’s randomized response technique. To study the performance of the newly developed stratified estimators, mean squared error and absolute bias were used as performance criteria. The proposed estimators were compared with the existing one. We observed that the proposed estimators are more sensitive to responses than the existing one at various sample sizes respectively.

scholarly journals Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling

2021 ◽  
Vol 5 (1) ◽  
pp. 192-199
Author(s):  
Ronald Onyango ◽  
◽  
Brian Oduor ◽  
Francis Odundo ◽  
◽  
...  
Keyword(s):  
Measurement Errors ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Real Data ◽  
Auxiliary Variable ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Joint Influence

The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.

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.

Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information

1970 ◽  
Vol 13 (3) ◽  
pp. 391-393 ◽  
Author(s):  
B. K. Kale
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Loss Function ◽  
Prior Information ◽  
Mean Squared Error ◽  
Closed Interval ◽  
Likelihood Estimator ◽  
Usual Estimator ◽  
Squared Error

Lehmann [1] in his lecture notes on estimation shows that for estimating the unknown mean of a normal distribution, N(θ, 1), the usual estimator is neither minimax nor admissible if it is known that θ belongs to a finite closed interval [a, b] and the loss function is squared error. It is shown that , the maximum likelihood estimator (MLE) of θ, has uniformly smaller mean squared error (MSE) than that of . It is natural to ask the question whether the MLE of θ in N(θ, 1) is admissible or not if it is known that θ ∊ [a, b]. The answer turns out to be negative and the purpose of this note is to present this result in a slightly generalized form.

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 Bayesian Estimation ofWarner’s Randomized Response Technique with Transmuted Kumaraswamy Prior

2021 ◽  
Author(s):  
Akinola Oladiran Adepetun ◽  
◽  
Bamidele Mustapha Oseni ◽  
Olusola Samuel Makinde ◽  
◽  
...  
Keyword(s):  
Tax Evasion ◽  
Unknown Parameter ◽  
Prior Information ◽  
Bayes Estimator ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Bayes Estimators ◽  
Population Proportion ◽  
Benchmark Data ◽  
Sensitive Attribute

In recent time, the Bayesian approach to randomized response technique has been used for estimating the population proportion especially of respondents possessing sensitive attributes such as induced abortion, tax evasion and shoplifting. This is done by combining suitable prior information about an unknown parameter of the population with the sample information for the estimation of the unknown parameter. In this study, possibility of using a transmuted Kumaraswamy prior is raised, yielding a new Bayes estimator for estimating population proportion of sensitive attribute for Warner’s randomized response technique. Consequently, the proposed Bayes estimator with transmuted Kumaraswamy prior is compared with existing Bayes estimators developed with a simple beta and Kumaraswamy priors in terms of their mean square error. The proposed estimator competes well with the existing estimators for some values of population proportion. The performances of Bayes estimators were also compared using some benchmark data.

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 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 Bayesian Analysis of Warner’s Randomized Response Technique

2017 ◽  
Vol 9 (1) ◽  
pp. 13-26
Author(s):  
A. O. Adepetun ◽  
A. A. Adewara
Keyword(s):  
Bayesian Analysis ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Sample Sizes ◽  
Large Sample ◽  
Population Proportion ◽  
Life Data ◽  
Sensitive Attribute ◽  
Alternative Beta ◽  
Survey Questionnaires

This paper proposed alternative beta estimators of the population proportion of a sensitive attribute when life data were obtained through the administration of survey questionnaires on abortion of some matured women. The results showed that the proposed alternative beta estimators were more efficient in capturing responses from respondents than the simple beta estimator proposed by Winkler and Franklin for relatively small, medium as well as large sample sizes respectively.

An Improved Two-stage Randomized Response Model for Estimating the Proportion of Sensitive Attribute

2021 ◽  
pp. 004912412110099
Author(s):  
Ghulam Narjis ◽  
Javid Shabbir
Keyword(s):  
Random Sampling ◽  
Stratified Random Sampling ◽  
Response Model ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Two Stage ◽  
Sensitive Attribute ◽  
Mean And Variance ◽  
Efficiency Comparison ◽  
Randomized Response Model

The randomized response technique (RRT) is an effective method designed to obtain the stigmatized information from respondents while assuring the privacy. In this study, we propose a new two-stage RRT model to estimate the prevalence of sensitive attribute ([Formula: see text]). A simulation study shows that the empirical mean and variance of proposed estimator are close to corresponding theoretical values. The utility of proposed two-stage RRT model under stratification is also explored. An efficiency comparison between proposed two-stage RRT model and some existing RRT models is carried out numerically under simple and stratified random sampling.

Minimax Shrunken Technique for Estimate Burr X Distribution Shape Parameter

2018 ◽  
pp. 484
Author(s):  
Abbas Najim Salman ◽  
Maymona M. Ameen ◽  
A. E. Abdul-Nabi
Keyword(s):  
Relative Efficiency ◽  
Prior Information ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
The Real ◽  
Squared Error ◽  
Distribution Shape ◽  
Original Estimate ◽  
Bias Ratio

      The present paper concern with minimax shrinkage estimator technique in order to estimate Burr X distribution shape parameter, when prior information about the real shape obtainable as original estimate while known scale parameter.  Derivation for Bias Ratio, Mean squared error and the Relative Efficiency equations.  Numerical results and conclusions for the expressions mentioned above were displayed. Comparisons for proposed estimator with most recent works were made.  

Sign in / Sign up

Export Citation Format

Share Document