Stratified Ranked Set Sampling Research Articles

On some efficient logarithmic type estimators under stratified ranked set sampling

On some efficient logarithmic type estimators under stratified ranked set sampling

Exploring the dependability of Combined Ratio Estimators in Stratified Ranked Set Sampling: Insights from COVID-19 data

In this study, we introduce a novel combined ratio type estimator within the framework of Stratified Ranked Set Sampling to estimate the population mean of the study variable by incorporating bivariate auxiliary information. We conduct a comprehensive comparative analysis, including traditional combined ratio, combined regression, Shabbir and Khan [13], and Bhushan and Kumar [37] estimators. We assess the bias and mean squared error of the proposed estimator under the initial degree of approximation. The data source consists of COVID-19 data up to July 2023. Through empirical investigation and simulation studies, our proposed estimator consistently demonstrates superior performance compared to its counterparts, exhibiting the highest relative efficiency. These findings underscore the practical significance of our research in public health and decision-making, emphasizing the potential of this estimator to provide more accurate and reliable estimates in various applications involving ranked set sampling and auxiliary information.

A Refinement of Ratio Estimation in Ranked Set Sampling and Stratified Ranked Set Sampling Approaches

Estimation of population mean is a persistent subject issue in sampling surveys and many discrete efforts have been paid by various researchers to enhance the precision of the estimates by utilizing the correlated auxiliary information. In connection with this an improved version of ratio estimator are presented in this paper under the ranked set sampling scheme and stratified ranked set sampling scheme. Comparison amongst estimators is made in terms of Mean Square Errors ( ) and Percentage Relative Efficiencies ( ). The expression for of the proposed estimator is pinned-down to first order of approximations. It turns out from both simulation studies as well as real data set that the proposed estimator dominates its existing counterpart estimators.

On stratified ranked set sampling for the quest of an optimal class of estimators

In the sample survey theory, the crux of survey practitioners is to provide “accurate” estimators of the parameter of choice. The conventional theory depends on the regression/difference estimators as they correspond to the best linear unbiased (BLU) estimators. This paper suggests some optimal classes of estimators by modifying the conventional estimators under stratified ranked set sampling (SRSS). The characteristics of the suggested estimators are established to the first-order approximation. The performance of the suggested class of estimators under SRSS has been theoretically and experimentally shown to be superior to traditional estimators, particularly regression (BLU) estimators.

Data-driven dynamic optimization for real-time parking reservation considering parking unpunctuality

This article examines a real-time parking reservation service that dynamically allocates a limited number of parking slots (which can be reused) to serve parking requests in a crowded area. The study takes into account two stochastic factors: (i) random arrivals of parking requests and (ii) driver parking unpunctuality, which are seldom simultaneously considered in the existing literature. This study formulates the dynamic parking resource allocation problem as a joint chance-constrained model to maximize the expected total revenue over a finite horizon. Due to the complex nature of the model considering the two stochastic factors, the study proposes a data-driven approach using joint chance constraint decomposition and sample average approximation to approximate the model to a deterministic mixed-integer programming model. Furthermore, a stratified ranked set sampling method is introduced to construct a high-quality sample set as the input to the deterministic model, and valid inequalities are designed to accelerate the solution process. Numerical experiments based on real-world data are conducted to validate the performance of the proposed approach under multiple parking scenarios and provide findings.

Two-stage approximation allocation approach for real-time parking reservations considering stochastic requests and reusable resources

The digital economy has greatly impacted the traditional parking industry. This study focuses on a real-time parking reservation system that allocates available parking slots (supplies) to serve the parking requests (demands) of drivers within a certain area. The challenge lies in dealing with the randomness of requests with varying parking durations and the reusability of parking resources, which have not been well researched. To address this problem, we propose a stochastic optimization model and a data-driven two-stage approximation approach. The first stage generates a pre-allocation scheme as a basis, while the second stage dynamically adjusts the scheme based on observed requests and available parking slots to improve the system’s performance throughout a finite operational horizon. The study has three main contributions. Firstly, this paper proposes a data-driven nonparametric approach based on sample average approximation (SAA) to solve the stochastic optimization model. Secondly, it develops a stratified ranked set sampling (SRSS) method to ensure the quality of the sample set and proves that the sample set sampled by the SRSS method is unbiased. Finally, an evaluation method is proposed to establish a confidence interval for the expected revenue obtained by the data-driven method. Experimental results based on real parking demand data show that our approach outperforms both a commonly used heuristic allocation policy in the parking industry and the standard SAA approach with two popular sampling methods and an evaluation method based on Student’s T-test in the literature.

Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling

This paper presents improved population mean estimators using auxiliary variables in Stratified Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by numerical illustrations and simulation study for which we have considered two populations.

Generalized Power Transformation Estimators in Stratified Ranked Set Sampling using Auxiliary Information

Auxiliary variable is commonly used in survey sampling to improve the precision of estimates. Whenever there is auxiliary information available, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. Stratified simple random sampling (SSRS) is used in certain types of surveys because it combines the conceptual simplicity of simple random sampling (SRS) with potentially significant gains in efficiency. It is a convenient technique to use whenever we wish to ensure that our sample is representative of the, population and also to obtain separate estimates for parameters of each sub domain of the population. Stratified Ranked Set Sampling combines the advantages of Stratification and Ranked set sampling (RSS) to obtain an unbiased estimator for the population mean, with potentially significant gains in efficiency. Under Stratified ranked set sampling scheme, we have suggested two general estimators using power transformation to estimate the population mean of the study variable. These methods are highly beneficial to the estimation based on Stratified Simple Random Sampling (SSRS). The first order approximation to the bias and mean square error (MSE) of the proposed estimators are obtained. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in Stratified simple random sampling. A numerical illustration is also included to demonstrate the merits of the proposed estimator using SRSS over the corresponding estimators in SSRS.

Partial stratified ranked set sampling scheme for estimation of population mean and median.

Ranked set sampling is an alternative to simple random sampling, which uses the least amount of money and time. The ranked set sampling (RSS) is modified to obtain a more efficient and cost-effective estimator of population parameters. This paper aims to bring a more efficient and cost-effective design than stratified ranked set sampling and simple random sampling. In some distributions, the suggested method used fewer sample units than stratified ranked set sampling and gives a more efficient estimation of population parameters. In symmetric distributions, the proposed design, called "partial stratified ranked set sampling" yields an unbiased estimator of the population mean. The design is illustrated with practical data of COVID-19 confirmed cases.

On Kernel-Based Estimator of Odds Ratio Using Different Stratified Sampling Schemes

The kernel-based estimator of Cochran Mantel-Haenszel odds ratio based on stratified simple and ranked set sampling is proposed. The expectation and variance of the estimator are analytically obtained. Using a simulation study, the estimator based on stratified ranked set sampling is more efficient than its counterpart based on stratified simple random sampling. Finally, the estimator's performance is investigated by using base deficit data.

On Some Improved Class of Estimators by Using Stratified Ranked Set Sampling

In this manuscript, we propose the combined and separate difference and ratio type estimators of population mean using stratified ranked set sampling. Additionally, several well-known estimators are identified as the sub-class of the suggested estimators. The characteristics of the suggested estimators have been analyzed and their effective performances are compared with the prominent estimators existing till date. Moreover, to prove the credibility of the theoretical findings, an extensive empirical study is administered over some real and hypothetically yielded symmetric and asymmetric populations.

On Efficient Estimation of the Population Mean under Stratified Ranked Set Sampling

This paper considers some efficient combined and separate classes of estimators of the population mean in the presence of bivariate auxiliary information under stratified ranked set sampling. The mean square error (MSE) expressions of the proffered combined and separate classes of estimators are derived to the first order of approximation. The theoretical conditions are obtained under which the proffered combined and separate classes of estimators perform better than the existing combined and separate class of estimators. Subsequently, numerical and simulation studies are performed using real and artificially generated populations. The numerical and simulation results are found to be rewarding, showing the superiority of the proffered estimators over the existing estimators.

ON EXTROPY PROPERTIES AND DISCRIMINATION INFORMATION OF DIFFERENT STRATIFIED SAMPLING SCHEMES

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.

On kernel-based quantile estimation using different stratified sampling schemes with optimal allocation

ABSTRACT The kernel-based estimators of a quantile function based on stratified samples of simple random sampling and ranked set sampling methods are proposed. The expectations and variances of the estimators are analytically obtained as well as their asymptotic distributions. Effect of imperfect ranking is considered in all analytically and numerically results. As theory and using a simulation study, it is shown that the estimator based on stratified ranked set sampling is more efficient than its counterpart on the basis of stratified simple random sampling. The simulation study is performed for three strata with small samples as well as large samples and for ten strata. Finally, the performance of the estimator is investigated by using China Health and Nutrition data set.

Estimation of population mean under different stratified ranked set sampling designs with simulation study Application to BMI Data

In this article, we have compared the performance ratio-type estimators in some stratified ranked set sampling methods. These sampling methods are stratified random sampling, stratified ranked set sampling, stratified double ranked set sampling and stratified median ranked set sampling. In these methods, the ratio type estimators using auxiliary variable information such as coefficient of variation and kurtosis are examined. We have used a real data set to see the performance of estimators. We use the data concerning body mass index (BMI) as a study variable and the age and the weight as auxiliary variables for 800 people in Turkey in 2014. We stratified the data set using gender. A simulation study is carried out to see performance of the proposed ratio type estimators in these stratified ranked set sampling designs. The performances of these estimators are compared in terms of mean squared error (MSE) and percent relative efficiency (PRE). The importance of this study is that, a detail simulation study is done using a real data set and compare these stratified sampling designs in a study in the sampling literature.

Stratified Two-Phase Ranked Set Sampling

We proposed an alternative two-phase stratified ranked set sampling. A comparison of the performances of the proposed estimators made by simulation studies using both real tree data collected by Platt et al. (1988) and generated bivariate normal data. It is found that the proposed two-phase stratified regression estimator fares better than those of the naive and Yu and Lam (1997) estimators.

On Kernel-Based Mode Estimation Using Different Stratified Sampling Designs

In the literature, the properties and the application of mode estimation is considered under simple random sampling and ranked set sampling (RSS). We investigate some of the asymptotic properties of kernel density-based mode estimation using stratified simple random sampling (SSRS) and stratified ranked set sampling designs (SRSS). We demonstrate that kernel density-based mode estimation using SRSS and SSRS is consistent, asymptotically normally distributed and using SRSS has smaller variance than that under SSRS. Improved performance of the mode estimation using SRSS compared to SSRS is supported through a simulation study. We will illustrate the method by using biomarker data collected in China Health and Nutrition Survey data.

Ratio estimators using stratified random sampling and stratified ranked set sampling

The aim of present study is to propose ratio estimators for the population mean using auxiliary information efficiently under stratified random sampling (SRS) and stratified ranked set sampling (SRSS). Here, bias and mean square error (MSE) for the proposed estimators have been obtained and find that the proposed estimator under SRSS is more efficient than the estimator under SRS. The results have been illustrated numerically through simulation study.

On quantiles estimation based on different stratified sampling with optimal allocation

ABSTRACTThis work considers the problem of estimating a quantile function based on different stratified sampling mechanism. First, we develop an estimate for population quantiles based on stratified simple random sampling (SSRS) and extend the discussion for stratified ranked set sampling (SRSS). Furthermore, the asymptotic behavior of the proposed estimators are presented. In addition, we derive an analytical expression for the optimal allocation under both sampling schemes. Simulation studies are designed to examine the performance of the proposed estimators under varying distributional assumptions. The efficiency of the proposed estimates is further illustrated by analyzing a real data set from CHNS.

Calibration estimator of population mean under stratified ranked set sampling design

ABSTRACTCalibration method adjusts the original design weights to improve the estimates by using auxiliary information. In this article we have proposed new calibration estimators under stratified ranked set sampling design and derive the estimator of variance of calibration estimator. A simulation study is carried out to see the performance of proposed estimators.