Estimation Of Finite Population Mean Research Articles

EFFICIENCY OF LOGARITHMIC RATIO CUM LOGARITHMIC PRODUCT ESTIMATORS IN DOUBLE SAMPLING USING IMPUTATION TECHNIQUES

In literature, there are many estimators of finite population mean, some of which are superior to the others. In practical situations, all the information on sample units may not be available due to non-response in sample surveys. Thus, our objective in this study is to get more precise estimators of the finite population mean of the study variable under two-phase sampling in case of missing data. Three new logarithmic ratio cum logarithmic product type imputation methods and corresponding point estimators have been introduced and observed to be better under two-phase sampling, which adds contribution to the field of imputation techniques. The bias and mean square errors of the proposed estimators are calculated in terms of population parameters. The performance of the proposed estimators is compared theoretically and empirically as well with existing traditional estimators.

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 finite population mean of a sensitive variable using three-stage optional RRT in the presence of non-response and measurement errors

The purpose of this study is to present a generalized class of estimators using the three-stage optional randomized response technique (RRT) in the presence of non-response and measurement errors on a sensitive study variable. The proposed estimator makes use of dual auxiliary information. The expression for the bias and mean square error of the proposed estimator are derived using Taylor series expansion. The proposed estimator's applicability is proven using real data sets. A numerical study is used to compare efficiency of the proposed estimator with adapted estimators of the finite population mean. The suggested estimator performs better than adapted ordinary, ratio, and exponential ratio-type estimators in the presence of both non-response and measurement errors. The efficiency of the proposed estimator of population mean declines as the inverse sampling rate, non-response rate, and sensitivity level of the survey question increase.

Efficient Classes of Robust Ratio Type Estimators of Mean and Variance in Adaptive Cluster Sampling

This paper proposes two classes of robust ratio type estimators of finite population mean and two classes of robust ratio type estimators of finite population variance using a single auxiliary variable under the adaptive cluster sampling design. Seven robust ratio type estimators have been developed from each class. The generalized expressions of bias and mean square error for each class have been derived up to the first order of approximation. The exact expressions of bias and MSE for all the developed estimators have been presented. Using simulation studies conducted in R programming, the high efficiency of all the developed estimators over similar existing estimators in adaptive cluster sampling has been demonstrated. . KEYWORDS :Adaptive cluster sampling, Classes of robust ratio type estimators, Hidden clustered data, Estimation of mean, Estimation of variance.

An Improved Product Estimator for Finite Population Mean in the Presence of Nonignorable Nonresponse

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Development of improved estimators of finite population mean in simple random sampling with dual auxiliaries and its application to real world problems

In general, the incorporation of supplementary information reduces the Mean Square Error (MSE) and, consequently, enhances the precision of estimating a population parameter. This improvement relies on the appropriate application of a suitable function, with careful consideration. This study introduces two innovative families of estimators for the finite population mean, both of which exhibit superior performance in scenarios involving dual auxiliary information in simple random sampling. Expressions up to the first-order approximation, for bias, and Mean Square Error were derived, and the conditions under which these proposed families surpassed the existing estimators. Our evaluation involved the use of both real and simulated data to compute the Mean Square Error and Percent Relative Efficiency (PRE) of the estimators. A comparative analysis revealed that under the specified conditions, both proposed families yielded more precise results.

Indirect Questioning Technique Related to Sensitive Quantitative Variables with Options for Direct, Randomized and Item Count Responses

Randomized Response (RR) Technique (RRT) pioneered by Warner (1965) is a useful tool to elicit responses on sensitive characteristics, such as induced abortions, drug abuse, drunken driving, total amount of counterfeit notes of a particular denomination held by individuals in the population, etc. There exists a huge literature on Randomized Response (RR) devices for estimation of finite population mean of quantitative variables, sensitive in nature mostly based on Eichhorn and Hayre (1983). Device-I and Device-II vide Chaudhuri and Christofides (2013) allow estimation of population mean of sensitive quantitative variables using sample chosen by a general sampling design. On the other hand, Item Count Technique (ICT), described elaborately in Chaudhuri and Christofides (2013), is an alternative to RRT for respondents who do not choose to provide RRs. While some respondents may find a variable as sensitive, others may find it innocuous enough to provide a direct response (DR) about his/her true value. In such a case, Optional Randomized Response (ORR) Technique (ORRT) with options for DR and RR was introduced by Chaudhuri and Mukherjee (1985). Pal (2007) proposed an ORR device which offers choices for RR and ICT to the respondents for giving their answers. A new ORRT with options for DR, RR and ICT was provided by Shaw and Pal (2021) for eliciting indirect responses on sensitive characteristics. As this device relates to estimation of population proportion of sensitive characteristics, an attempt has been made to extend it for sensitive quantitative variables. Further, to take care of individuals’ varying choices for DR, RR and ICT and to protect the privacy of the respondents’ choices, this paper develops an ORR device allowing the respondents chosen by a general sampling design, to choose any one of the three options according to their choices. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 155-170

Weighted Strategy for Estimation of Finite Population Mean in Presence of Auxiliary Information

ABSTRACT In sample designs, it is commonly recognized that using auxiliary information significantly increases an estimator’s precision. This manuscript introduces an weighted strategy for computing the finite population mean using auxiliary information in sample surveys. The equations for the mean squared error (MSE) of the proposed estimator are derived under large sampling approximation. A graphical representation of efficiency comparison is provided to show the ranges where the proposed estimator performs more efficiently. Additionally, a numerical analysis is conducted to evaluate the performance of the suggested estimator using actual datasets.

Almost Unbiased Optimum Ratio-type Estimator for Estimating Population Mean in Stratified Sampling in Presence of Non-response

In this paper we have proposed classes of ratio-type estimators for finite population mean in presence of non-response in stratified sampling. The properties of the estimators have been discussed. We have also derived optimum choices of scalar constant to reduce the bias in the estimators which make suggested classes of estimators almost unbiased. The expressions of mean square error (MSE) have been derived up to the first order of approximation. We have compared our proposed classes of estimators with natural ratio estimators and with estimator under complete response. Results are also supported by empirical study.

Calibration estimator for a sensitive variable using dual auxiliary information under measurement errors

In survey research, it is commonly assumed that all the observations are measured accurately. However, in practice, this assumption is not achieved due to many reasons, so it causes measurement errors to be inevitably present in the sample estimation. This article addresses the problem of estimation of finite population mean under stratified random sampling in the presence of measurement errors. A calibration estimator is proposed for the sensitive variable by utilizing suitable calibration techniques, which can be applied to obtain the optimal strata weight. The calibration estimator not only incorporates the auxiliary information but also the ranks of the auxiliary variable. Expressions for bias and mean square error are derived up to first order of approximation. Simulation studies and real-life datasets are used to assess the performances of the proposed estimator by comparing them with the contemporary estimators in the presence and absence of measurement errors. The theoretical and empirical studies demonstrate that the proposed calibration estimator consistently outperforms classical mean, usual ratio, conventional difference, Khail randomized response estimators.

Incorporating the neutrosophic framework into kernel regression for predictive mean estimation

In traditional statistics, all research endeavors revolve around utilizing precise, crisp data for the predictive estimation of population mean in survey sampling, when the supplementary information is accessible. However, these types of estimates often suffer from bias. The major aim is to uncover the most accurate estimates for the unknown value of the population mean while minimizing the mean square error (MSE). We have employed the neutrosophic approach, which is the extension of classical statistics that deals with the uncertain, vague, and indeterminate information, and proposed a neutrosophic predictive estimator of finite population mean using the kernel regression. The proposed estimator does not yield a single numerical value but instead provides an interval range within which the population parameter is likely to exist. This approach enhances the efficiency of the estimators by offering an estimated interval that encompasses the unknown value of the population mean with the least possible mean squared error (MSE). The simulation-based efficiency of the proposed estimator is discussed using the Sine, Bump and real-time temperature data set of Islamabad by using symmetric (Gaussian) kernel. The proposed non-parametric neutrosophic estimator has shown more effective results under the various bandwidth selectors than the adapted neutrosophic estimators.

Geographically weighted ridge regression estimator of finite population mean to tackle multicollinearity in survey sampling

Geographically weighted ridge regression estimator of finite population mean to tackle multicollinearity in survey sampling

Power ratio cum median-based ratio estimator of finite population mean with known population median

The search for an efficient estimator of the finite population mean has been a critical problem to the sample survey research community. This study is motivated by the fact that the conducted literature review showed that no research has developed such an average ratio estimator of the population mean that would utilize both the population and the sample medians of study variable, as well as the Srivastava (1967) estimator at a time. In this paper we proposed the power ratio cum median-based ratio estimator of the finite population mean, which is a function of two ratio estimators in the form of an average. The estimator assumes the population to be homogeneous and skewed. The properties (i.e. the Bias and the Mean Squared Error – MSE) of the proposed estimator were derived alongside its asymptotically optimum MSE. We demonstrated the efficiency of the proposed estimator jointly with its efficiency conditions by comparing it to selected estimators described in the literature. Empirically, a real-life dataset from the literature and a simulation study from two skewed distributions (Gamma and Weibull) were used to examine the efficiency gain. The empirical analysis and simulation study demonstrated that the efficiency gain is significant. Hence, the practical application of the proposed estimator is recommended, especially in socio-economic surveys.

Calibration Ratio Type Estimator of Finite Population Mean for Stratified Random Sampling

Calibration Ratio Type Estimator of Finite Population Mean for Stratified Random Sampling

A Generalized Class of Log-Type Estimators of Finite Population Mean Based on Correlation Coefficient

In sampling theory, it is a popular trend to use auxiliary information to obtain more efficient estimators for the population parameters to increase the precision of the estimator. Estimators obtained using auxiliary information are supposed to be more efficient than the estimators obtained without using auxiliary information. The ratio, regression, product and difference methods take advantage of the auxiliary information at the estimation stage. Therefore, this study considered a generalized class of log-type estimators of finite population mean based on correlation coefficient as the proposed estimator for estimating the population mean of the study variable. It has been shown that the generalized class of log-type estimators has lesser mean square errors (MSEs) under the optimum values of the characterizing scalar as compared to some of the commonly used related estimators available in the literature. Further, an extension of the proposed generalized class of log-type estimators using multiple auxiliary variables such as coefficient of variation, coefficient of kurtosis , and correlation coefficient. have also base initiated in this dissertation. The expressions for the properties of the proposed family of estimators, that is; Bias and Mean Square Error (MSE), were derived to the first degree of approximation. We also obtained the optimum Mean Square Error (MSEopt.), and theoretical comparisons were made with the related existing estimators in literature. Following theoretical comparisons, it was demonstrated that the proposed family of estimators was more efficient than various related existing estimators compared with, under the obtained conditions.

Estimation of finite population mean using double sampling under probability proportional to size sampling in the presence of extreme values

Values that are too large or small enough can be found in many data sets. Therefore, the estimator can yield ambiguous findings if several of the incredible deals are picked for the sample. When such extreme values occur, we propose improved estimators to determine the finite population means using double sampling based on probability proportional to size sampling (PPS). The properties of estimators are obtained up to the first order of approximations. When the size of the units varies widely, the PPS sampling technique may be employed. To determine the values of Pi when using PPS, we must be acquainted with the aggregate of the auxiliary variable Xi. However the designs and estimation techniques we have looked at so far are unsuccessful and are less effective when this information is difficult to locate or when other information is missing. The two-phase approach is preferable and more feasible in these kinds of circumstances. To demonstrate how effectively the recommended estimators performed, we used three actual data sets. We show mathematically and theoretically that the suggested estimators outperform alternative estimators.

Predictive Estimation of Finite Population Mean in Case of Missing Data Under Two-phase Sampling

The present paper deals with the problem of estimation of finite population mean of study variable using two auxiliary variables in two-phase sampling scheme using predictive approach in case of missing values of the study variable and unknown population mean of first auxiliary variable. Four classes of such estimators have been proposed using this predictive approach. The expressions of bias and mean square errors are derived up to first order of approximation. The optimal values of the constants involved in the proposed classes of estimators have been obtained and thus minimum mean square errors of the proposed classes are obtained in this study. The empirical and graphical comparisons with regression type estimators (under single phase and double phase sampling scheme) and also among themselves have been made for evaluating the performance of the proposed classes for different choices of non-responding units. Five real data sets and three simulated data sets following normal distribution have been used to evaluate the performance of the proposed classes. Numerical findings confirm the theoretical results obtained regarding superiority of proposed classes of estimators over the conventional regression type estimators in terms of percent relative efficiencies.

Modified Exponential Ratio-Type Estimator of Population Mean in Stratified Sampling using Calibration Approach

In this paper, the problem of estimation of finite population mean in stratified random sampling is considered. Two improved exponential logarithmic type calibration estimators for finite population mean have been proposed for stratified random sampling when auxiliary information related to variable under study is available for each stratum. To judge the performance of the proposed estimators, a simulation study has been carried out in R-software using two datasets, one real and another one artificial generated population. The proposed estimators have also been compared with the estimators developed by Bahl and Tuteja [1] and Singh [17] in case of stratified random sampling.

New generalized class of estimators for estimation of finite population mean based on probability proportional to size sampling using two auxiliary variables: A simulation study.

This article aims to suggest a new generalized class of estimators based on probability proportional to size sampling using two auxiliary variables. The numerical expressions for the bias and mean squared error (MSE) are derived up to the first order of approximation. Four actual data sets are used to examine the performances of a new improved generalized class of estimators. From the results of real data sets, it is examined that the suggested estimator gives the minimum MSE and the percentage relative efficiency is higher than all existing estimators, which shows the importance of the new generalized class of estimators. To check the strength and generalizability of our proposed class of estimators, a simulation study is also accompanied. The consequence of the simulation study shows the worth of newly found proposed class estimators. Overall, we get to the conclusion that the proposed estimator outperforms as compared to all other estimators taken into account in this study.

A New Class of Quantile Regression Ratio-Type Estimators for Finite Population Mean in Stratified Random Sampling

Quantile regression is one of the alternative regression techniques used when the assumptions of classical regression analysis are not met, and it estimates the values of the study variable in various quantiles of the distribution. This study proposes ratio-type estimators of a population mean using the information on quantile regression for stratified random sampling. The proposed ratio-type estimators are investigated with the help of the mean square error equations. Efficiency comparisons between the proposed estimators and classical estimators are presented in certain conditions. Under these obtained conditions, it is seen that the proposed estimators outperform the classical estimators. In addition, the theoretical results are supported by a real data application.