Estimation Of Population Variance Research Articles

Enhanced Estimation of Population Variance under Simple Random Sampling with an Application to Real Data

In this paper, we present an enhanced class of estimators for finite population variance under simple random sampling that incorporates an auxiliary information. The equations for bias and mean square error of the proposed estimators are produced up to the first order of approximation. Some well-known estimators are found as a special case of the proposed estimators for suitably chosen values of the scalars. The effectiveness of the proposed estimators is calculated in relation to the existing estimators both theoretically and empirically using five real data sets. The empirical results exhibit the superiority of the suggested estimators over to the existing estimators in each population.. KEYWORDS :Auxiliary variable, Mean square error, Variance estimation, Class of estimators.

An Estimator of Population Variance Using Multi-Auxiliary Information

In this article, an estimator of population variance using multi-auxiliary information has been proposed. It is seen that under certain conditions, the proposed estimator is less biased and more efficiency than existing estimators. Theoretical results are supported numerically. Moreover, a simulation study also has been made.

An efficient estimator of population variance of a sensitive variable with a new randomized response technique

In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model.

Improved estimation of population variance in stratified successive sampling using calibrated weights under non-response

This paper introduces a new method to estimate the population variance of a study variable in stratified successive sampling over two occasions, while accounting for random non-response. The method uses a logarithmic type estimator and leverages information from a highly positively correlated auxiliary variable. The paper also presents calibrated weights for the new estimator and examines its properties through numerical and simulation studies. The results indicate that the suggested estimator is more effective than the standard estimator for estimating the population variance.

A general class of improved population variance estimators under non-sampling errors using calibrated weights in stratified sampling.

This paper proposes a new calibration estimator for population variance within a stratified two-phase sampling design. It takes into account random non-response and measurement errors, specifically applying this method to estimate the variance in Gas turbine exhaust pressure data. The study integrates additional information from two highly positively correlated auxiliary variables to develop a general class of estimators tailored for the stratified two-phase sampling scheme. The properties of these estimators, in terms of their biases and mean square errors, have been thoroughly examined and extensively analyzed through numerical and simulation studies. Furthermore, the calibrated weights of the strata are derived. The proposed estimators outperform the natural estimator of population variance. Finally, suitable recommendations have been made for survey statisticians intending to apply these findings to real-life problems.

Enhanced Variance Estimation Techniques for Addressing Non-Response and Measurement Error Situations

The use of relevant information from auxiliary variables at the estimation stage and design stage to obtain reliable and efficient estimates is a common practice in a sample survey. Several Estimators of population variance have been suggested. However, these estimators do not consider the situation of non-response due to non-availability of respondents, refusal to respond, presence of hard- core respondents or due to non-understanding of the question thereby, reducing the efficiency of the estimators and the parameters of the auxiliary variable X̄ , S2x used are sensitive to outliers or extreme values which can either lead to underestimation or overestimation. To address the aforementioned observations, classes of variance estimators under the simultaneous influence of non-response and measurement errors using outlier-free parameters as well as calibration approaches were proposed. The properties (Bias and MSE) of the modified estimators were derived up to the first order of approximation using the Taylor series approach. The efficiency conditions of the proposed estimators over the existing estimators considered in the study were established. The empirical studies were conducted using simulation and the results revealed that the proposed class of estimators have minimum MSEs and higher PREs among all the competing estimators. These imply that the proposed estimators are more efficient and can produce a better estimate of the population mean compared to other existing estimators considered in the study.

Improved estimators of population variance using robust measures in case of missing data

In this paper, an attempt has been made in proposing some improved estimators of finite population variance when random non-response is present in the study variable, on the estimators given by Sharma and Singh (2018). Four improved regression type estimators have been proposed using information on two auxiliary variables, one of which has missing values in the data, using two-phase sampling scheme. Different robust regression methods have been applied on the proposed techniques so as to improve the efficiency of the estimators in case of outliers. It has been observed that robust estimators are more efficient than the proposed ones under some conditions. All the proposed estimators are compared with existing estimators for different values of probability of non-response and the results are verified by using empirical and simulation studies.

Applying ORRT for the estimation of population variance of sensitive variable

The current work is driven to provide a collaborated variance estimator for the estimation of population variance by employing optional randomized response technique (ORRT) in order to boost variance estimation. The formulations of bias and mean squared error of the recommended variance estimator under ORRT are established to the first degree of approximation. To assess the performance of the suggested estimator by utilizing a unified measure and efficiency of the estimator, a simulation study is conducted by using R software. According to the findings and graphical representations, it is observed that our proposed estimator is much more convenient than competing estimator(s).

Efficient estimation of population variance of a sensitive variable using a new scrambling response model

This study introduces a pioneering scrambling response model tailored for handling sensitive variables. Subsequently, a generalized estimator for variance estimation, relying on two auxiliary information sources, is developed following this novel model. Analytical expressions for bias, mean square error, and minimum mean square error are meticulously derived up to the first order of approximation, shedding light on the estimator’s statistical performance. Comprehensive simulation experiments and empirical analysis unveil compelling results. The proposed generalized estimator, operating under both scrambling response models, consistently exhibits minimal mean square error, surpassing existing estimation techniques. Furthermore, this study evaluates the level of privacy protection afforded to respondents using this model, employing a robust framework of simulations and empirical studies.

Comparative Analysis of Variance Estimation Methods in Two-Phase Sampling: A Focus on Regression-cum-Exponential Estimators with Multiple Auxiliaries

In this study, we introduce a regression-cum-exponential estimator designed for estimating population variance. Specifically, we focus on the estimation of unknown population variance in a two-phase sampling setup, considering the use of multiple auxiliary variables. We derive and discuss various cases pertaining to this estimation framework. Additionally, we compare the asymptotic properties of existing approaches with those of our proposed estimator. This allows us to assess the performance and efficiency of the different methods. Finally, we conduct a simulation study to evaluate the performance of our proposed estimator in finite samples, specifically utilizing multi-auxiliary variables. This empirical analysis provides insights into the practical effectiveness of the estimators.

Generalized Estimator of Population Variance utilizing Auxiliary Information in Simple Random Sampling Scheme

In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.

A Modified Ratio Estimator in the Presence of Tri-Mean and Interquartile Range for the Estimation of Population Variance

A Modified Ratio Estimator in the Presence of Tri-Mean and Interquartile Range for the Estimation of Population Variance

Generalized Ratio-Product cum Regression Variance Estimator in Two-Phase Sampling

This study develops a flexible and efficient generalized ratio-product cum regression-type estimator of population variance utilizing auxiliary variable in two-phase sampling that incorporates the properties of ratio-type and product-type estimators. The properties of the estimator were derived using first order approximation. The theoretical conditions under which the precision and the flexibility of the estimator is better than some classical estimators are also provided. Empirical evidence from five real datasets suggests that the proposed estimator outperforms the classical variance, ratio variance, product, and exponential ratio type estimators in terms of precision and efficiency. The estimator can be utilized to provide better variance estimates for various phenomena such as inflation variation, exchange rate variation and standard of living variation for better policymaking.

Estimation of population variance under ranked set sampling method by using the ratio of supplementary information with study variable.

In biological and medical research, the cost and collateral damage caused during the collection and measurement of a sample are the reasons behinda compromise on the inference with a fixed and accepted approximation error. The ranked set sampling (RSS) performs better in such scenarios, andthe use of auxiliary information even enhances the performance of the estimators. Inthis study, two generalized classes of estimatorsareproposedto estimate the population variance using RSS and information of auxiliary variable. The bias and mean square errors ofthe proposed classes of estimators are derived up to first order of approximation. Some special cases of one ofthe proposed class ofestimatorsare also considered in the presence of available population parameters. A simulation study was conductedto see the performance of the members of the proposed family by using various sample sizes. The real-life dataapplication is done to estimate the variance of gestational age of fetuses with supplementary information. The results showed that RSS design is a more accurate method than simple random sampling, to determine the population variance of hard-to-measure or destructive sampling units.

On enhanced estimation and monitoring of population variance using robust auxiliary parameters based estimators

SummarySearching for efficient estimators of population variance as compared to sample variance has been the key area of interest of the researchers. Auxiliary variable has helped very much in finding estimators more efficient than sample variance. Auxiliary variable is greatly correlated with main study variable. Many authors including Isaki (J Am Stat Assoc 1983, 78, 117) used positively correlated auxiliary variable in the form of various conventional and non‐conventional auxiliary parameters and suggested different ratio type estimators of population variance. In this article, we have suggested a naïve class of variance estimators based on some robust auxiliary parameters, which deals with the outliers in the data. The properties including bias and Mean Square Error (MSE) of suggested family of estimators are studied up to first order of approximation. The theoretical as well as empirical comparison of introduced family of estimators is carried out with competing variance estimators. The estimator with the least MSE is recommended in different areas of applications. At last, the Shewhart type control charts based on the proposed estimators are also studies for application in quality control.

Modified unbiased estimators for population variance: An application for COVID-19 deaths in Russia.

SummaryThe article deal with the class unbiased forms of the variance estimators using Hartley–Ross type in the simple random sampling. The mean squared error (since it is an unbiased estimator, variance is calculated) of the suggested, up to the first order of approximation, is derived. The proposed estimator using COVID‐19 data in Russia has been proven to be more efficient than the considered estimators under the conditions. Thus, it allows us to see the variance estimator that best predicts the change according to federal regions in Russia's number of COVID‐19 deaths. This study also provides an unbiased family of estimators that are more efficient than existing estimators, which estimate the variance of the total death number of COVID‐19 based on the daily new cases number. The most important difference of this article from other studies in the literature is that it is the first study to examine the variance of the COVID‐19 cumulative mortality value in terms of variance estimation using the simple random sampling method with the auxiliary variable.

On the estimation of finite population variance for a mail survey design in the presence of non-response using new conventional and calibrated estimators

In this paper, we proposed new conventional unbiased and calibration estimators for estimating finite population variance for a Mail Survey Design characterized by the presence of non-response in practice. The properties of the proposed estimators are studied theoretically and numerically. Empirical studies were conducted using two each of existing and simulated data to illustrate the performance of proposed estimators over existing ones. The results of both theoretical and numerical comparison depicted the superiority of proposed estimators for estimating population variance for a Mail Survey Design characterized by non-response.

DIFFERENCE-CUM-EXPONENTIAL EFFICIENT ESTIMATOR OF POPULATION VARIANCE

In the current investigation, we have suggested a Difference Cum-Exponential Type Efficient Estimator of Population variance of the study variable using information on the auxiliary variable. Up to the first order of approximation, the proposed estimator's bias and mean square error (MSE) expressions are derived and suggested optimum estimator is also found, with its optimal qualities are investigated. The suggested estimator is proven to be more competent than sample variance, classic ratio estimators based on Isaki , Singh et al. and Kadilar and Cingi estimators in [1-3]. Numerical study is also carried out by using real data sets.

QUESTING ELEVATED FAMILY OF PRODUCT ESTIMATORS OF POPULATION MEAN USING AUXILIARY VARIABLES

The present manuscript deals with the enhanced estimation of population mean using the known negatively correlated auxiliary variable. We introduce a naïve class of product type estimators of population variance utilizing known auxiliary parameters. The expressions for the bias and the mean squared error (MSE) of the proposed family of estimators are retained up to the first order of approximation. The optimal values of the characterizing constants are obtained by the method of Maxima-Minima. The least value of MSE of the introduced class is obtained for these optimal values of the constants. The suggested family of estimators is compared with the competing product estimators of the population mean. The efficiency conditions are also obtained and these are verified through the real data set. The estimators with the lesser MSE are recommended for the practical utility in different areas of applications.

Jackknife winsorized variance estimator under imputed data

Abstract In the present study, we consider the problem of missing and extreme values for the estimation of population variance. The presence of extreme values either in the study variable, or the auxiliary variable, or in both of them, can adversely affect the performance of the estimation procedure. We consider three different situations for the presence of extreme values and also consider jackknife variance estimators for the population variance by handling these extreme values under stratified random sampling. Bootstrap technique ABB is carried out to understand the relative relationship more precisely.