Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme

An improved estimator of finite population mean when using two auxiliary attributes

In the present paper, we have proposed some improved ratio and regression-type estimators of the finite population mean utilizing the information on two auxiliary variables in the presence of non-response. The two-phase sampling scheme has been used to accomplish the job of estimating the desired parameter. The expressions for the basic properties such as bias and mean square error (MSE) of the proposed estimators have been derived up to the first order of approximation. A comparative study of the proposed estimators with some existing estimators has also been carried out through a real data set.

Sampling methods are important factors that can potentially limit the accuracy of predictions of spatial distribution patterns. A 10 ha tobacco-planted field was selected to compared the accuracy in predicting the spatial distribution of soil properties by using ordinary kriging and cross validation methods between grid sampling and simple random sampling scheme (SRS). To achieve this objective, we collected soil samples from the topsoil (0-20 cm) in March 2012. Sample numbers of grid sampling and SRS were both 115 points each. Accuracies of spatial interpolation using the two sampling schemes were then evaluated based on validation samples (36 points) and deviations of the estimates. The results suggested that soil pH and nitrate-N (NO 3 -N) had low variation, whereas all other soil properties exhibited medium variation. Soil pH, organic matter (OM), total nitrogen (TN), cation exchange capacity (CEC), total phosphorus (TP) and available phosphorus (AP) matched the spherical model, whereas the remaining variables fit an exponential model with both sampling methods. The interpolation error of soil pH, TP, and AP was the lowest in SRS. The errors of interpolation for OM, CEC, TN, available potassium (AK) and total potassium (TK) were the lowest for grid sampling. The interpolation precisions of the soil NO 3 -N showed no significant differences between the two sampling schemes. Considering our data on interpolation precision and the importance of minerals for cultivation of flue-cured tobacco, the grid-sampling scheme should be used in tobacco-planted fields to determine the spatial distribution of soil properties. The grid-sampling method can be applied in a practical and cost-effective manner to facilitate soil sampling in tobacco-planted field.

Neutrosophic statistics is a generalization of classical statistics and fuzzy logic that addresses ambiguous, imprecise, vague and indeterminate data. The concept of Neutrosophic statistics has been introduced in the development of estimators of population mean. The concept has extended to the development with estimators with two auxiliary variables. Some of the existing estimators of population mean with two auxiliary variables are functions of unknown parameters of auxiliary variables which makes them impracticable in real life situations. These existing estimators are either ratio-based, product-based or ratio-product-based which are less efficient when the correlation between the study and auxiliary variable is strong and negative. Therefore, to address the problem this study intends to proposed new classes of population mean estimators which are efficient and independent of unknown parameters. The proposed estimators are regression-based estimators which are applicable for either positive or negatives, weak or strong correlation. The properties (Biases and MSEs) of the proposed estimators are derived up to the first order of approximation. The theoretical efficiency conditions of the proposed estimators over some existing related estimators were established. The theoretical conclusions are validated by the empirical analysis, which made use of the simulated data. Empirical studies were conducted to assess the performances (Biases, MSEs and PREs) of the proposed estimator relative to existing estimators. The result revealed that the proposed estimators have minimum biases, minimum MSEs and higher PREs with exception of few cases compared to that of existing competing estimators considered in the study. These results demonstrate the superiority of the proposed estimator over the existing estimators in terms of the accuracy, efficiency and efficiency gain in the estimation of the population mean under Neutrosophic settings.

In modern age of information technology, data is available everywhere in huge amount. Every sector generates lot of data every day. The investigation of each unit of data is not feasible due to limited resources like time, labor, and cost. In such situations, survey sampling is recommended to draw the information about the population parameters. Therefore, the main objective of present study is to develop an estimation method for obtaining the information about population parameter. We propose an optimum estimator for enhanced estimation of population mean in simple random sampling by utilizing the information of the two auxiliary attribute. The expression for bias, mean squared error (MSE) and minimum mean squared error of the proposed estimator are derived up to the first order of approximation and it is shown that the proposed estimator under derived conditions perform better than the existing estimators theoretically. Four population are demonstrated to assess the performance as well as applicability of the proposed estimator. The percentage relative efficiency (PRE) of proposed estimator for all the populations is 209.533, 163.852, 210.398 and 340.578, respectively. The numerical illustrations confirm that the proposed estimator dominates over the existing estimators.•The main objective of present study is to propose a new estimator/method for estimation of population mean using two auxiliary attributes under simple random sampling.•The bias and mean square error of the proposed estimator/method is derived and compared with the existing estimators to compare the efficiency theoretically.•Applications of the proposed method/estimator is highlighted using thorough the real data sets of various sectors.

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.

An improved family of estimators of finite population mean based on the auxiliary attribute

In the present study we propose a new estimator for population mean Y of the study variable y in the case of stratified random sampling using the information based on auxiliary variable x. An expression for the mean squared error (MSE) of the proposed estimator is derived up to the first order of approximation. The theoretical conditions have also been verified by a numerical example. An empirical study demonstrates the efficiency of the suggested estimator over sample mean estimator, usual separate ratio, separate product estimator and other proposed estimators.

Mean of ratios or ratio of means or both?

This paper presents some efficient classes of estimators of population mean on current occasion in the presence of random non-response under a two-phase successive sampling set-up. The suggested classes of estimators are proposed for simple random sampling under various situations of non-response. The properties of proposed estimators have been discussed up to first order of approximation. The efficiency of the presented estimators has been contrasted with the estimators for the complete response scenarios. Two real and two artificially generated data sets are used. The efficacy of the proposed classes of estimators over the existing estimators is checked theoretically and empirically. The numerical comparison supports the proposed estimators.

This paper suggests some estimators for population mean of the study variable in simple random sampling and two-phase sampling using information on an auxiliary variable under second order approximation. Bahl and Tuteja (1991) and Singh et al. (2008) proposed some efficient estimators and studied the properties of the estimators to the first order of approximation. In this paper, we have tried to find out the second order biases and mean square errors of these estimators using information on auxiliary variable based on simple random sampling and two-phase sampling. Finally, an empirical study is carried out to judge the merits of the estimators over others under first and second order of approximation.

The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.

In this paper, we introduce a ratio estimator for finite population mean in the context of optional RRT models. We discuss the Bias and the Mean Square Error (MSE) of our proposed ratio estimator, correct up to first order of approximation, and present its comparison with some other estimators. A simulation study is also conducted to validate the theoretical results. Both the theoretical and the empirical results show that the proposed ratio estimator is more efficient than the competing estimators.

Double sampling scheme is used when cheap auxiliary variables may be measured to improve the estimation of a finite population parameter. Several estimators for population mean, ratio of means and variance are available, when two dependent samples are drawn. However, there are few proposals for the case of independent samples. In this paper both cases of dependent and independent samples are dealt with. A general approach for estimating a finite population parameter is given, showing that all the proposed estimators are particular cases of the same general class. The minimum variance bound for any estimator in this class is provided (at the first order of approximation). Furthermore, an optimal estimator which reaches this minimum is found.

ABSTRACTWhenever there is auxiliary information available in any form, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. When there exists enough amount of correlation between the study and the auxiliary variables, and parallel to these associations, the ranks of the auxiliary variables are also correlated with the study variable, which can be used a valuable device for enhancing the precision of an estimator accordingly. This article addresses the problem of estimating the finite population mean that utilizes the complementary information in the presence of (i) the auxiliary variable and (ii) the ranks of the auxiliary variable for non response. We suggest an improved estimator for estimating the finite population mean using the auxiliary information in the presence of non response. Expressions for bias and mean squared error of considered estimators are derived up to the first order of approximation. The performance of estimators is compared theoretically and numerically. A numerical study is carried out to evaluate the performances of estimators. It is observed that the proposed estimator is more efficient than the usual sample mean and the regression estimators, and some other families of ratio and exponential type of estimators.