Estimation Of Population Mean Research Articles

Calibration Estimators with Different Types of Distance Measures Under Stratified Sampling in the Presence of Measurement Error

The calibration method is used in stratified random sampling in the presence of measurement error to achieve optimum strata weights for better precision. In this study we attempt to analyze the behaviour of calibration estimators with different types of distance measures in the presence of measurement error for the estimation of population mean under stratified random sampling. The proposed estimators are compared with the estimators in the absence of measurement error. A simulation study has been carried out to evaluate the proposed estimators.

An improved variant of quantitative randomized response techniques using forced responses

The randomized response technique has gained a wide popularity among survey researchers over the past few decades. Randomized response procedure is applicable in a variety of fields including sociology, psychology, business, and education, etc. It is a useful method which helps the researcher in dealing with the high non-response rates in sample surveys on sensitive issues such as monthly income, traffic rules violations, income tax amount, and expenditure on luxury items, etc. We introduce an optimal scrambling technique which uses forced responses. The algebraic properties of the estimator of population mean using the suggested technique have been derived. For the purpose of comparison with existing models, the different measures of model-evaluation have been obtained. Our analysis suggests that the new quantitative technique using forced responses is better than the available scrambling techniques not only in efficiency, but also in the combined metric of model’s efficiency and level of privacy, which make it more useful than the available models for practical problems. Using real-world example, we illustrate its practical implementation to sensitive sample surveys.

Optimizing population mean estimation under ranked set sampling with applications to Engineering

This article aims to develop two novel mean estimators of finite populations under ranked set sampling. The suggested estimators result in a high-efficiency gain due to their efficient formulation by taking the linear combination of classical estimators using optimization constants. We also discuss the theoretical properties and derive bias and mean squared error up to the first order of approximation. To theoretically validate our proposed estimators, we derive the conditions under which our estimators prevail over the competing estimators. The findings suggest that when ranked set sampling is implemented effectively, it saves cost and improves precision, serving as a potent instrument for improved decision-making, specifically in engineering applications, such as environmental monitoring, resource management, and quality control. An empirical and simulation study has been conducted using real and synthetic data to validate our methodology empirically. The suggested estimators offer a significant contribution to survey sampling in estimating mean under ranked set sampling. Further, the proposed estimator can be seamlessly adapted in other sampling designs such as simple random sampling, stratified random sampling, cluster sampling, etc, as well as in estimating other parameters such as variance, skewness, coefficient of correlation, etc. in various domains.

Improved weak lensing photometric redshift calibration via StratLearn and hierarchical modelling

ABSTRACT Discrepancies between cosmological parameter estimates from cosmic shear surveys and from recent Planck cosmic microwave background measurements challenge the ability of the highly successful $\Lambda$CDM model to describe the nature of the Universe. To rule out systematic biases in cosmic shear survey analyses, accurate redshift calibration within tomographic bins is key. In this paper, we improve photo-z calibration via Bayesian hierarchical modeling of full galaxy photo-z conditional densities, by employing ${\it StratLearn}$, a recently developed statistical methodology, which accounts for systematic differences in the distribution of the spectroscopic training/source set and the photometric target set. Using realistic simulations that were designed to resemble the KiDS + VIKING-450 data set, we show that ${\it StratLearn}$-estimated conditional densities improve the galaxy tomographic bin assignment, and that our ${\it StratLearn}$-Bayesian framework leads to nearly unbiased estimates of the target population means. This leads to a factor of $\sim 2$ improvement upon often used and state-of-the-art photo-z calibration methods. Our approach delivers a maximum bias per tomographic bin of $\Delta \langle z \rangle = 0.0095 \pm 0.0089$, with an average absolute bias of $0.0052 \pm 0.0067$ across the five tomographic bins.

The impact of age and renal function on the pharmacokinetics and protein binding characteristics of fludarabine in paediatric and adult patients undergoing allogeneic haematopoietic stem cell transplantation conditioning

Abstract Aim To evaluate the population pharmacokinetics of unbound F-Ara-A (the circulating metabolite of fludarabine) in 211 patients (age range, 0.1–63.4 years) undergoing allogeneic haematopoietic stem cell transplantation conditioning. Methods Total (n = 2480) and unbound (n = 1403) F-Ara-A concentrations were measured in blood samples collected at timed intervals after fludarabine doses ranging from 10 to 50 mg/m2 and infused over 0.42–1.5 h. A three-compartment population pharmacokinetic model was developed based on unbound plasma concentrations and used to estimate F-Ara-A unbound pharmacokinetic parameters and fraction unbound (fu). A number of covariates, including glomerular filtration rate (GFR) and post-menstrual age (PMA), were evaluated for inclusion in the model. Results The base population mean estimates ± relative standard error (%RSE) for unbound clearance from the central compartment (CLu) and inter-compartmental clearances (Q2u, Q3u) were 3.42 ± 3%, 6.54 ± 24% and 1.47 ± 16% L/h/70 kg, respectively. The population mean estimates (%RSE) for the unbound volume of distribution into the central (V1u) and peripheral compartments (V2u, V3u) were 9.65 ± 8%, 8.17 ± 9% and 16.4 ± 10% L/70 kg, respectively, and that for fu was 0.877 ± 1%. Covariate model development involved differentiating F-Ara-A CLu into non-renal (1.81 ± 9% L/h/70 kg) and renal components (1.02 ± 9%*GFR L/h/70 kg). A sigmoidal maturation factor was applied to renal CLu, with population mean estimates for the Hill exponent and PMA at 50% mature of 2.97 ± 4% and 69.1 ± 8% weeks, respectively. Conclusion Patient age and GFR are predictors of unbound F-Ara-A CLu. This has the potential to impact dose requirements. Dose individualisation by target concentration intervention will be facilitated by this model once it is externally validated.

Improved Ratio-type Exponential Estimator for Estimating Population Mean in Ranked Set Sampling

In this paper we propose a ratio-type exponential estimator for estimating population mean of the study variable under Ranked set sampling when auxiliary information is known. The bias and Mean square error of the proposed estimator has been derived up to the first degree of approximation. A simulation study has been carried out to judge the performance of the newly proposed estimator along with existing estimators. It is obtained that the proposed estimator is more efficient as compared to the competing estimators.

Design based study for adjusting non-response while estimating population mean

Design based study for adjusting non-response while estimating population mean

Preliminary estimators of population mean using ranked set sampling in the presence of measurement error and non-response error with applications and simulation study

In order to estimate the population mean in the presence of both non-response and measurement errors that are uncorrelated, the paper presents some novel estimators employing ranked set sampling by utilizing auxiliary information. Up to the first order of approximation, the equations for the bias and mean squared error of the suggested estimators are produced, and it is found that the proposed estimators outperform the other existing estimators analysed in this study. Investigations using simulation studies and numerical examples show how well the suggested estimators perform in the presence of measurement and non-response errors. The relative efficiency of the suggested estimators compared to the existing estimators has been expressed as a percentage, and the impact of measurement errors has been expressed as a percentage computation of measurement errors.

Efficient population mean estimation via stratified sampling with dual auxiliary information: A real estate perspective

Auxiliary information is an essential component in the field of survey sampling since it enables precise estimation of population parameters like mean, variance, distribution function, and so on, which in turn guarantees the best possible outcomes. In order to estimate the population mean of a study variable, this study makes use of auxiliary information in a two-fold approach. Through a stratified random sampling scheme, we introduce a novel class of estimators that utilize auxiliary information and their corresponding ranks. By conducting a thorough evaluation based on metrics such as mean square error and percentage relative efficiency, these proposed estimators have been shown to be effective in the estimation process. Empirical validation is conducted using a real dataset sourced from the domain of real estate. Exploring the relationship between Assessed Value (X) and Sale Amount (Y) during a five-year period extending from 2017 to 2021 is the primary emphasis of the empirical validation process, which is carried out with the assistance of a real dataset of real estate data. Furthermore, in order to demonstrate that our suggested estimator is superior to conventional unbiased estimators, as well as traditional regression estimators and other estimators that have been considered in the literature, a full simulation analysis is carried out. Our proposed estimator appears to be the most effective choice after being subjected to a comparison study against a variety of preexisting approaches. The findings of this study not only make a significant contribution to the development of the methodology of survey sampling but also offer vital insights for predictive modeling within the real estate sector.

New Modification of Ranked Set Sampling for Estimating Population Mean: Neutrosophic Median Ranked Set Sampling with an Application to Demographic Data

The study addressed the limitations of classical statistical methods when dealing with ambiguous data, emphasizing the importance of adopting neutrosophic statistics as a more effective alternative. Classical methods falter in managing uncertainty inherent in such data, necessitating a shift towards methodologies like neutrosophic statistics. To address this gap, the research introduced a novel sampling approach called “neutrosophic median ranked set sampling” and incorporated neutrosophic estimators tailored for estimating the population mean in the presence of ambiguity. This modification aims to address the inherent challenges associated with estimating the population mean when dealing with neutrosophic data. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Additionally, neutrosophic estimators were developed to leverage auxiliary information within the framework of median-ranked set sampling, enhancing the accuracy of population mean estimation under uncertain conditions. The methods employed involved modifying traditional ranked set sampling techniques to accommodate neutrosophic data characteristics. Bias and mean squared error equations for the suggested estimators were provided, offering insights into their theoretical underpinnings. To illustrate the effectiveness and practical applications of the proposed methodology and estimators, a numerical demonstration and simulation study have been conducted using the R programming language. The key results highlighted the superior performance of the proposed estimators compared to existing alternatives, as demonstrated through comprehensive evaluations based on mean squared error and percentage relative efficiency criteria. The conclusions drawn underscored the effectiveness of the neutrosophic median ranked set sampling approach and suggested estimators in estimating the population mean under conditions of uncertainty, particularly when utilizing neutrosophic auxiliary information and validated real-life applicability. The methodology and estimators presented in the study were shown to yield interval-based results, providing a more realistic representation of uncertainty associated with population parameters. This interval estimation, coupled with minimum mean squared error considerations, enhanced the efficacy of the estimators in determining population mean values. The novelty of the work lies in its introduction of a tailored sampling approach and estimators designed specifically for neutrosophic data, filling a significant gap in the literature. By extending classical statistics to accommodate ambiguity, the study offers a substantial advancement in statistical methodology, particularly in domains where precise data is scarce and uncertainty is prevalent. Furthermore, the empirical validation through numerical demonstrations and simulation studies using the R programming language adds robustness to the proposed methodology and contributes to its practical applicability.

Novel logarithmic imputation procedures using multi auxiliary information under ranked set sampling

Ranked set sampling (RSS) is known to increase the efficiency of the estimators while comparing it with simple random sampling. The problem of missingness creates a gap in the information that needs to be addressed before proceeding for estimation. Negligible amount of work has been carried out to deal with missingness utilizing RSS. This paper proposes some logarithmic type methods of imputation for the estimation of population mean under RSS using auxiliary information. The properties of the suggested imputation procedures are examined. A simulation study is accomplished to show that the proposed imputation procedures exhibit better results in comparison to some of the existing imputation procedures. Few real applications of the proposed imputation procedures is also provided to generalize the simulation study.

Exponential Ratio Class of Estimators of Finite Population Mean Using Deciles of an Auxiliary Variable

Practitioners of survey sampling have been working to reduce bias and increase efficiency in the estimation of finite population parameters. The present work aims at developing an exponential ratio class of finite population mean estimators with deciles of an auxiliary variable. Using the Taylor's series technique, the mean square error (MSE) of the developed estimators was obtained up to the first order of approximation. The study's suggested estimators outperform competing estimators, according to the findings of a numerical analysis that was done on them in comparison to the existing estimators that were taken into consideration.

Estimation of Population Mean Using Some Improved Imputation Methods for Missing Data in Sample Surveys

. In this research article, we present novel imputation methods designed to address missing data challenges in sample surveys. We then introduce innovative estimation procedures for calculating population means based on these methods. Our study thoroughly examines the properties of these new estimation procedures, assessing their biases and mean square errors. Through the use of both real and simulated data sets, we demonstrate the superior performance of our proposed estimators compared to existing methods in similar scenarios. In conclusion, we offer practical recommendations for survey practitioners.

An effective computational and simulation study for population mean estimation on current occasion

An effective computational and simulation study for population mean estimation on current occasion

Understanding stunting and its determinant among children in the most populous state of India using estimation of population mean under ranked set sampling in the presence of missing data

ABSTRACT In real-life scenarios, encountering data with missing values is common, and if not managed carefully from the outset of a study, it can lead to significant biases in survey estimates. Various methods exist for imputing missing values in sampling procedures. Ranked set sampling (RSS) is widely recognized for its superior efficiency compared to simple random sampling. However, limited research has been conducted on ranked set sampling in the presence of missing data. This article introduces novel imputation methods designed to estimate population means in the context of missing data under RSS. These innovative estimators are developed by integrating ratio, exponential, and logarithmic estimators judiciously. Expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation. Through simulation studies and an application to stunting and its determinants among children in Uttar Pradesh, India’s most populous state, the effectiveness of the suggested estimators in handling missing data is demonstrated. Numerical examples involving stunting in Uttar Pradesh, as well as simulated data generated using R software, confirm the superior performance of the proposed estimators over existing methods, as evidenced by comparisons of percentage relative efficiency and mean squared error. The results are promising, indicating improvement over all existing imputation methods. Additionally, pertinent recommendations are provided for survey professionals regarding future research.

Modified median quartile double ranked set sampling for estimation of population mean

Environmental monitoring and assessment aim to gather data economically, without bias, using efficient and cost-effective sampling methods. One such traditional method is Ranked Set Sampling (RSS), often employed to achieve observational economy. This article introduces an innovative two-stage sampling approach for ranked set sampling (RSS) to get a more precise estimate of the population mean. Modified Median Quartile Double Ranked Set Sampling (MMQDRSS) highlights the ranked base technique's potential as a cost-effective sampling method. To evaluate the performance of the proposed estimator by using real-life data and conducting a simulation study to compare the relative efficiency of the proposed estimator with some existing methods.

Superpopulation model inference for non-probability samples under informative sampling

Non-probability samples have been extensively applied in many various fields in recent years. However, it is difficult to infer the population from non-probability samples since selection probabilities of non-probability samples is unknown. Superpopulation modeling has been recently explored to make inference from non-probability samples. However, the existing superpopulation model approaches rely mostly on the noninformative sampling assumption. When sampling is informative, the sample distribution differs from the population distribution. Ignoring this point may result in biased estimation. In this paper, taking into account the informative sampling scheme, a superpopulation model approach for non-probability samples is proposed. Exponential model, logistic model and probit model are established to explain the informative sampling mechanism, respectively. The sample likelihood is derived to estimate the superpopulation model parameters for non-probability samples under various informative sampling models. The population mean estimator can be obtained based on the fitted superpopulation model from non-probability samples under different informative sampling approaches. The theoretical properties of the proposed estimator are established. Simulation results illustrate the performance of our proposed method for different informative sampling models and sample sizes. Also, the proposed method is applied to the data from the National Health and Nutrition Examination Survey.

Improved memory-type ratio estimator for population mean in stratified random sampling under linear and non-linear cost functions

This paper offers an improved memory-type ratio estimator in stratified random sampling under linear and non-linear cost functions. The issue is given as all integer non-linear programming problems (AINLPPs). The sampling properties mainly the bias and the mean squared error of the introduced estimator are derived up to the first order of approximation. The optimum value of the characterizing scalar is obtained by the Lagrange method of maxima–minima. The least value of the MSE of the suggested estimator is also obtained for this optimum value of the charactering constant. The suggested estimator is compared both theoretically and empirically with the competing estimators. Under this setup, the optimum allocation with mean square error of the suggested estimator is attained, and the estimator is compared to other comparable estimators. The AINLPP is solved using the genetic programming approach, which is applied to both actual and simulated data sets from a bivariate normal distribution.

A Class of Ratio Estimators for Estimating Population Mean Using a Transformed Auxiliary Variable Under Stratified Random Sampling

A Class of Ratio Estimators for Estimating Population Mean Using a Transformed Auxiliary Variable Under Stratified Random Sampling

Efficient and alternative approaches for imputing missing data to estimate population mean

Efficient and alternative approaches for imputing missing data to estimate population mean