Improved estimation of population parameter in the existence of non-response using auxiliary information

Kadilar and Cingi [Ratio estimators in simple random sampling, Appl. Math. Comput. 151 (3) (2004), pp. 893–902] introduced some ratio-type estimators of finite population mean under simple random sampling. Recently, Kadilar and Cingi [New ratio estimators using correlation coefficient, Interstat 4 (2006), pp. 1–11] have suggested another form of ratio-type estimators by modifying the estimator developed by Singh and Tailor [Use of known correlation coefficient in estimating the finite population mean, Stat. Transit. 6 (2003), pp. 655–560]. Kadilar and Cingi [Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett. 19 (1) (2006), pp. 75–79] have suggested yet another class of ratio-type estimators by taking a weighted average of the two known classes of estimators referenced above. In this article, we propose an alternative form of ratio-type estimators which are better than the competing ratio, regression, and other ratio-type estimators considered here. The results are also supported by the analysis of three real data sets that were considered by Kadilar and Cingi.

Recently, Shabbir and Gupta [Shabbir, J. and Gupta, S. (2011). On estimating finite population mean in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 40(2), 199–212] defined a class of ratio type exponential estimators of population mean under a very specific linear transformation of auxiliary variable. In the present article, we propose a generalized class of ratio type exponential estimators of population mean in simple random sampling under a very general linear transformation of auxiliary variable. Shabbir and Gupta's [Shabbir, J. and Gupta, S. (2011). On estimating finite population mean in simple and stratified random sampling. Communications in Statistics-Theory and Methods, 40(2), 199–212] class of estimators is a particular member of our proposed class of estimators. It has been found that the optimal estimator of our proposed generalized class of estimators is always more efficient than almost all the existing estimators defined under the same situations. Moreover, in comparison to a few existing estimators, our proposed estimator becomes more efficient under some simple conditions. Theoretical results obtained in the article have been verified by taking a numerical illustration. Finally, a simulation study has been carried out to see the relative performance of our proposed estimator with respect to some existing estimators which are less efficient under certain conditions as compared to the proposed estimator.

ABSTRACTWe propose an improved difference-cum-exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling using two auxiliary variables. We obtain properties of the estimators up to first order of approximation. The proposed class of estimators is found to be more efficient than the usual sample mean estimator, ratio estimator, exponential ratio type estimator, usual two difference type estimators, Rao (1991) estimator, Gupta and Shabbir (2008) estimator, and Grover and Kaur (2011) estimator. We use six real data sets in simple random sampling and two in stratified sampling for numerical comparisons.

Accurate estimation of the finite population mean is a fundamental challenge in survey sampling, especially when dealing with large or complex populations. Traditional methods like simple random sampling may not always provide reliable or efficient estimates in such cases. Motivated by this, the current study explores complex sampling techniques to improve the precision and accuracy of mean estimators. Specifically, we employ two-stage and three-stage cluster sampling methods to develop unbiased estimators for the finite population mean. Building upon these, the next phase of the study formulates unbiased mean estimators using stratified two- and three-stage cluster sampling. To further enhance the precision of these estimators, a ranked-set sampling strategy is applied to the secondary and tertiary sampling stages. Additionally, unbiased variance estimators corresponding to the proposed mean estimators are derived. Real-world datasets are utilized to demonstrate the application of these complex survey sampling methodologies, with results showing that the mean estimates derived using ranked set sampling are more accurate than those obtained via simple random sampling.

In this paper, classes of separate and combined regression-cum-ratio estimators have been proposed for estimating the finite population mean in stratified random sampling. The expressions for biases and mean square errors (MSEs) of the proposed classes have been derived to the first order of approximation. It has also been verified that the proposed classes of estimators, at their optimum conditions, are equivalent to the separate regression estimator. The proposed classes of estimators have been compared with the other existing estimators using MSE criterion, and the conditions under which the proposed classes perform better have been obtained. Numerical illustrations are given in support of theoretical findings. Relevance of the work The estimation theory is relevant to various interdisciplinary areas of research including economics, clinical trials, population studies, engineering, agriculture, etc. Also, the problem of estimation of mean is of huge importance in research, for instance, the estimation of: average agricultural production, average life span of persons in a region, mean concentration of dissolved minerals in water, and much more. For the estimation of mean, several design-based approaches are being widely used, for instance, simple random sampling, stratified random sampling, two-phase sampling, etc. If the population under study is homogeneous, then the simple random sampling design is used at the estimation stage. However, in various practical situations, the research study is based on the heterogeneous population, and in that case the stratified random sampling procedure is preferable over the simple random sampling. Considering the above fact, an attempt has been made in this paper to develop the classes of generalized estimators for the mean of the variable under study using stratified random sampling.

ABSTRACTIn this article, we propose a new class of estimators to estimate the finite population mean by using two auxiliary variables under two different sampling schemes such as simple random sampling and stratified random sampling. The proposed class of estimators gives minimum mean squared error as compared to all other considered estimators. Some real data sets are used to observe the performances of the estimators. We show numerically that the proposed class of estimators performs better as compared to all other competitor estimators.

In sample surveys, non-sampling errors are inherent due to non-response and measurement errors. Non-response occurred when the response is not available from respondent due to not being at home, no willingness to answer etc. Another error is the difference between the observed and actual values is known as measurement error. For dealing with such kind of errors1, we advocate the use of factor-type estimator for estimation of population mean in this manuscript and the expressions of the bias, mean square error (MSE) and optimum mean square error of suggested estimator has been derived. An empirical study is also performed over a real data set and bias, mean squared error and efficiency calculated for comparison purpose by simulation.

In the existing survey sampling literature, the ratio-type estimators are an obvious choice to estimate the finite population mean when auxiliary information related to the study variable is readily available. Typically, auxiliary information is incorporated into ratio-type estimators by using conventional measures such as mean, range, coefficient of kurtosis, coefficient of skewness and coefficient of correlation, etc. which are less efficient when extreme observation are present in the data. This study provides a remedy and enhances the efficiency of the ratio-type estimators of population mean in the presence of extreme observations by proposing dual auxiliary variables based exponential-cum-ratio class of estimators which integrates both conventional and non-conventional measures under simple random sampling without replacement. The expression of the mean squared error and theoretical efficiency conditions for proposed class of estimators have been obtained for comparison purposes. A simulation study was carried out based on contaminated normal distribution and the robustness of the proposed estimators has been assessed in the presence of extreme observations. For practical implementation, six real data sets have been used to compare the performance of the proposed estimators with competing estimators to support the theoretical results. The theoretical and empirical results suggest that the proposed estimators are more precise than usual mean as well as existing estimators’ ratio-type considered in this study.

The use of extreme values of the auxiliary variable is sometimes more beneficial to get the high efficiency of the estimators, and the study variable can have a correlation with the rank of the decently correlated auxiliary variable. As a result, it can be regarded as additional data for the study variable that can be used to improve the estimators’ efficiency. When the knowledge of the minimum and maximum values, as well as the rankings of the auxiliary variable, is known, various better estimators for calculating the finite population mean of the research variable based on extreme values under simple random sampling are proposed in this paper. The suggested estimators’ bias and mean squared error expressions are derived using first-order approximation. The recommended estimators have been compared mathematically to the current estimators. The suggested estimators are more exact in terms of relative efficiency than the other estimators addressed here, as shown by simulation and real datasets used to demonstrate the estimation of a limited population mean based on extreme values.

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.

ABSTRACTThis article suggests the class of estimators of population mean of study variable using various parameters related to an auxiliary variable with its properties in simple random sampling. It has been identified that the some existing estimator/classes of estimators are members of suggested class. It has been found theoretically as well as empirically that the suggested class is better than the existing methods.

This paper proposes an improved general family of ratio-type estimators using the coefficient of skewness of an auxiliary variable for estimating finite population mean under simple random sampling. Bias, mean squared error (MSE) and minimum MSE of the proposed family are derived up to the first degree of approximation. It is found that proposed family behaves better than competing estimators under some simple conditions. Theoretical findings are confirmed with numerical illustration using three natural populations. In addition, Monte Carlo simulation study on a real data set also proves the potential of the proposed family against the common unbiased estimator, traditional ratio estimator and estimators by Yan and Tian (CCIS 106:103–110, 2010).

The most popular methods for sensitive study are regression estimation methods that use standard regression coefficients. When it comes to survey researchers, mean estimation is an important issue. The vast majority of population mean estimation methods that can be found in sampling theory are meant only to be utilized with non-sensitive data-sets. When the variable that is important is sensitive, such as drug usage, illegal income, abortion, exam cheating, the amount of income tax due, employee rule-breaking, etc., these estimation methods cannot operate efficiently. In this article, we propose a novel method for computing the population mean using exponential technique of robust-type regression estimators for scrambled response model (SRM) under simple random sampling (SRS). The mean square error (MSE) equation is generated using a first-order approximation and examined with existing estimating techniques in order to evaluate the efficacy of the new approach. Additionally, the proposed estimator's percentage relative efficiency (PRE) is determined compared to other estimators. The effectiveness of the proposed method is demonstrated using real data sets. According to the results, the suggested estimator performs better than other estimators in the literature.

In the present study, we have suggested an improved class of estimator for estimating populating mean with the help of two auxiliary variable using simple random sampling and stratified random sampling. We have derived the mean square error and bias of the suggested estimator, and theoretically showed that our proposed estimator performs better than some given existing estimators. In addition, we support this theoretical result with the help of numerical examples. 1. SOME ESTIMATORS UNDER SIMPLE RANDOM SAMPLING In the theory of sample survey, we can increase the precision or accuracy of suggested estimator by using auxiliary information but when no additional information related to auxiliary variable is available then the simplest estimator of population mean is the sample mean. When study variable Y is highly positively correlated with the auxiliary variable(X) then we use ratio estimator; when it is negatively correlated then we use product estimator for estimating population parameters. In large scale survey, we often collect data on more than one auxiliary variable(s) and some of these may be correlated with y. (1), (2), (3), (4), Dianna and Perri(2007), Singh et al. (2011), (5), Malik and Singh (5, 6), Singh and Singh (7) considered some estimators which utilised information on several auxiliary variables which are correlated with the study variable. Bahl and Tuteja (8) suggested an exponential ratio type estimator. Singh (9) proposed a ratio cum product type estimator. Kadilar and Cingi(10) have proposed ratio in difference type estimator. Motivated by these authors we have suggested an improved different type of estimator for estimating population mean using simple and stratified random sampling. For the different choices of constants different family and some well-known existing estimators may be generated from the proposed family of estimators.

Population mean is an important characteristic from many perspectives in statistical methodology. In this connection, many separate ratio type estimators of population mean have been developed by the researchers to gain more precision and efficiency available in the literature. This study suggests a new class of logarithmic separate ratio-product type estimators of a finite population mean in stratified random sampling using one auxiliary variable to achieve enhanced precision and efficiency. The mean square error expression for the proposed class of estimators and some selected estimates are derived till first order of approximation. Three real data sets and a simulation study reveal that the proposed estimators outperform other estimators used in this analysis.