On Estimating Population Means of Two-Sensitive Variables With Ranked Set Sampling Design

2022 ◽  
pp. 42-61
Author(s):  
Agustin Santiago Moreno ◽  
Khalid Ul Islam Rather
Keyword(s):  
Empirical Evidence ◽  
Simulation Study ◽  
Random Sampling ◽  
Relative Efficiency ◽  
Convex Combination ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Population Means ◽  
Sampling Schemes

In this chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.

On Estimating Population Means of Two-Sensitive Variables With Ranked Set Sampling Design

2022 ◽  
pp. 104-140
Author(s):  
Shivacharan Rao Chitneni ◽  
Stephen A. Sedory ◽  
Sarjinder Singh
Keyword(s):  
Empirical Evidence ◽  
Simulation Study ◽  
Random Sampling ◽  
Relative Efficiency ◽  
Convex Combination ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Population Means ◽  
Sampling Schemes

In the chapter, the authors consider the problem of estimating the population means of two sensitive variables by making use of ranked set sampling. The final estimators are unbiased and the variance expressions that they derive show that ranked set sampling is more efficient than simple random sampling. A convex combination of the variance expressions of the resultant estimators is minimized in order to suggest optimal sample sizes for both sampling schemes. The relative efficiency of the proposed estimators is then compared to the corresponding estimators for simple random sampling based on simulation study and real data applications. SAS codes utilized in the simulation to collect the empirical evidence and application are included.

scholarly journals Bayesian Analysis of Finite Populations under Simple Random Sampling

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 318
Author(s):  
Manuel Mendoza ◽  
Alberto Contreras-Cristán ◽  
Eduardo Gutiérrez-Peña
Keyword(s):  
Bayesian Analysis ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Survey Sampling ◽  
Finite Populations ◽  
Population Means ◽  
Sampling Schemes ◽  
Nonparametric Approach ◽  
Conventional Procedure ◽  
Continuous And Discrete Variables

Statistical methods to produce inferences based on samples from finite populations have been available for at least 70 years. Topics such as Survey Sampling and Sampling Theory have become part of the mainstream of the statistical methodology. A wide variety of sampling schemes as well as estimators are now part of the statistical folklore. On the other hand, while the Bayesian approach is now a well-established paradigm with implications in almost every field of the statistical arena, there does not seem to exist a conventional procedure—able to deal with both continuous and discrete variables—that can be used as a kind of default for Bayesian survey sampling, even in the simple random sampling case. In this paper, the Bayesian analysis of samples from finite populations is discussed, its relationship with the notion of superpopulation is reviewed, and a nonparametric approach is proposed. Our proposal can produce inferences for population quantiles and similar quantities of interest in the same way as for population means and totals. Moreover, it can provide results relatively quickly, which may prove crucial in certain contexts such as the analysis of quick counts in electoral settings.

Stratified Ranked Set Sampling With Missing Observations for Estimating the Difference

2022 ◽  
pp. 209-232
Author(s):  
Carlos N. Bouza-Herrera
Keyword(s):  
Random Sampling ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Missing Observations ◽  
Seminal Paper ◽  
Sample Error ◽  
The Difference ◽  
Stratified Ranked Set Sampling ◽  
Stratified Model

The authors develop the estimation of the difference of means of a pair of variables X and Y when we deal with missing observations. A seminal paper in this line is due to Bouza and Prabhu-Ajgaonkar when the sample and the subsamples are selected using simple random sampling. In this this chapter, the authors consider the use of ranked set-sampling for estimating the difference when we deal with a stratified population. The sample error is deduced. Numerical comparisons with the classic stratified model are developed using simulated and real data.

scholarly journals Maximum likelihood estimation in location-scale families using varied L ranked set sampling

2020 ◽  
Author(s):  
Amer Al-Omari
Keyword(s):  
Maximum Likelihood ◽  
Random Sampling ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Sampling Schemes ◽  
Scale Parameters ◽  
Insight Into ◽  
Family Of Distributions

Recently, a generalized ranked set sampling (RSS) scheme has been introduced which encompasses several existing RSS schemes, namely varied L RSS (VLRSS), and it provides more precise estimators of the population mean than the estimators with the traditional simple random sampling (SRS) and RSS schemes. In this paper, we extend the work and consider the maximum likelihood estimators (MLEs) of the location and scale parameters when sampling from a location-scale family of distributions. In order to give more insight into the performance of VLRSS with respect to SRS and RSS schemes, the asymptotic relative precisions of the MLEs using VLRSS relative to that using SRS and RSS are compared for some usual location-scale distributions. It turns out that the MLEs with VLRSS are more precise than those with the existing sampling schemes.

scholarly journals Estimation of the Exponential Pareto Distribution’s Parameters under Ranked and Double Ranked Set Sampling Designs

2021 ◽  
pp. 169-184
Author(s):  
Mohamed H. Sabry ◽  
Ehab Mohamed Almetwally
Keyword(s):  
Random Sampling ◽  
Relative Efficiency ◽  
Pareto Distribution ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Mean Square ◽  
Distribution Parameters ◽  
Mean Square Errors

In this paper, the derivation of the likelihood function for parameter estimation based on double ranked set sampling (DRSS) designs used by Sabry el.al.; (2019) for the estimation of the parameters of the power generalized Weibull distribution is considered. The developed likelihood function is then used for the estimation of the exponential Pareto distribution parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) designs. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different designs. The relative efficiency of the DRSS estimates with respect to other designs was found to be higher in case of the exponential Pareto distribution (EP).

scholarly journals Sensitive proportion in ranked set sampling

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256699
Author(s):  
Azhar Mehmood Abbasi ◽  
Muhammad Yousaf Shad
Keyword(s):  
Numerical Integration ◽  
Random Sampling ◽  
Unbiased Estimator ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Ratio Method ◽  
Integration Technique ◽  
Sampling Cost ◽  
Rank Set Sampling

This paper considers the concomitant-based rank set sampling (CRSS) for estimation of the sensitive proportion. It is shown that CRSS procedure provides an unbiased estimator of the population sensitive proportion, and it is always more precise than corresponding sample sensitive proportion (Warner SL (1965)) that based on simple random sampling (SRS) without increasing sampling cost. Additionally, a new estimator based on ratio method is introduced using CRSS protocol, preserving the respondent’s confidentiality through a randomizing device. The numerical results of these estimators are obtained by using numerical integration technique. An application to real data is also given to support the methods.

Item Count Technique in Ranked Set Sampling

2022 ◽  
pp. 26-41
Author(s):  
Beatriz Cobo ◽  
Elvira Pelle
Keyword(s):  
Simulation Study ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Alternative Methods ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Sampling Without Replacement ◽  
Questioning Techniques ◽  
Item Count Technique

In situations where the estimation of the proportion of sensitive variables relies on the observations of real measurements that are difficult to obtain, there is a need to combine indirect questioning techniques. In the present work, the authors will focus on the item count technique, with alternative methods of sampling, such as the ranked set sampling. They are based on the idea proposed by Santiago et al., which combines the randomized response technique proposed by Warner together with ranked set sampling. The authors will carry out a simulation study to compare the item count technique under ranked set sampling and under simple random sampling without replacement.

ON EXTROPY PROPERTIES AND DISCRIMINATION INFORMATION OF DIFFERENT STRATIFIED SAMPLING SCHEMES

2021 ◽  
pp. 1-16
Author(s):  
Abbas Eftekharian ◽  
Guoxin Qiu
Keyword(s):  
Random Sampling ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Stochastic Orders ◽  
Data Sets ◽  
Sampling Schemes ◽  
Discrimination Information ◽  
Imperfect Ranking ◽  
Stratified Ranked Set Sampling ◽  
Better Than

Ranked set sampling (RSS) and some of its variants are sampling designs that are applied widely in different areas. When the underlying population contains different subpopulations, we can use stratified ranked set sampling (SRSS) which combines the advantages of stratification with RSS. In the present paper, we consider the information content of SRSS in terms of extropy measure. Some results using stochastic orders properties are obtained. The effect of imperfect ranking on discrimination information is analytically investigated. It is proved that discrimination information between the perfect SRSS and simple random sampling (SRS) data sets performs better than that of between the imperfect SRSS and SRS data sets.

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.

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