Modified Classes of Regression-Type Estimators of Population Mean in the Presences of Auxiliary Attribute (original) (raw)
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A Family of Estimators of Population Mean Using Information on Auxiliary Attribute
2006
In practice, the information regarding the population proportion possessing certain attribute is easily available. So for estimating the population mean Y of study variable y, a family of estimators of Y has been proposed by using the known information of population proportion possessing an attribute (highly correlated with y). The expressions for the mean square error of the estimators of the proposed family and its minimum value have been obtained. It has been shown that the optimum estimator of the proposed family of estimators of Y is always better than the mean per unit estimator. The results have also been extended for the case of the double sampling design. The results obtained have been illustrated numerically by taking some empirical populations considered in the literature.
Oriental Journal of Physical Sciences
In this research, estimators are suggested to improve modified classes of regression type estimators of finite population mean. The essence of proposing the estimators is as a result of the assumption that there may be weak relationship between study variable and auxiliary attribute. Properties (Biases and MSEs) of the proposed estimators are procured using Taylor series method. The efficiency conditions under which the proposed estimators are better than other related ones are established. Empirical findings are incentive and the results shown that the proposed estimators are more proficient compare to the existing estimators considered in the study.
A New Regression Type Estimator and Its Application in Survey Sampling
Open Journal of Statistics , 2020
In the present time, a large number of modified estimators have been proposed by authors to obtain efficiency. In this study, we suggested an alternative regression type estimator for estimating finite population means when there is either a positive or negative correlation between study variables and auxiliary variables. We obtained bias and mean square error equation of the proposed estimator ignoring the first-order approximation and found the theoretical conditions that make proposed estimator more efficient than simple random sampling mean estimator, product estimator and ratio estimator. In addition, these conditions are supported by a numerical example and it has been concluded that the proposed estimator performed better comparing with the usual simple random sampling mean estimator, ratio estimator and product estimator.
Oriental Journal of Physical Sciences, 2023
Some existing estimators based on auxiliary attribute have been proposed by many authors. In this paper, we use the concept of power transformation to modify some existing estimators in order to obtain estimators that are applicable when there is positive or negative correlation between the study and auxiliary variable. The properties (Biases and MSEs) of the proposed estimators were derived up to the first order of approximation using Taylor series approach. The efficiency comparison of the proposed estimators over some existing estimators considered in the study were established. The empirical studies were conducted using existing population parameters to investigate the proficiency of the proposed estimators over some existing estimators. The results revealed that the proposed estimators have minimum Mean Square Errors and higher Percentage Relative Efficiencies than the conventional and other competing estimators in the study. These implies that the proposed estimators are more efficient and can produce better estimates of the population mean compared to the existing estimators considered in the study.
On Improved Estimation of Population Mean using Qualitative Auxiliary Information
This paper deals with the estimation of population mean of the variable under study by improved ratio-product type exponential estimator using qualitative auxiliary information. The expression for the bias and mean squared error (MSE) of the proposed estimators has been derived to the first order of approximation. A comparative approach has been adopted to study the efficiency of proposed and previous estimators. The present estimators provide us significant improvement over previous estimators leading to the better perspective of application in various applied areas. The numerical demonstration has been presented to elucidate the novelty of paper. 1. Introduction The use of supplementary (auxiliary) information has been widely discussed in sampling theory. Auxiliary variables are in use in survey sampling to obtain improved sampling designs and to achieve higher precision in the estimates of some population parameters such as the mean or the variance of the variable under study. This information may be used at both the stage of designing (leading for instance, to stratification, systematic or probability proportional to size sampling designs) and estimation stage. It is well established that when the auxiliary information is to be used at the estimation stage, the ratio, product and regression methods of estimation are widely used in many situations. The estimation of the population mean is a burning issue in sampling theory and many efforts have been made to improve the precision of the estimates. In survey sampling literature, a great variety of techniques for using auxiliary information by means of ratio, product and regression methods has been used. Particularly, in the presence of multi-auxiliary variables, a wide variety of estimators have been proposed, following different ideas, and linking together ratio, product or regression estimators, each one exploiting the variables one at a time. The first attempt was made by Cochran (1940) to investigate the problem of estimation of population mean when auxiliary variables are present and he proposed the usual ratio estimator of population mean. Robson (1957) and Murthy (1964) worked out independently on usual product estimator of population mean. Olkin (1958) also used auxiliary variables to estimate population mean of variable under study. He considered the linear combination of ratio estimators based on each auxiliary variable separately making use of information related to the supplementary characteristics having positive correlation with the variable under consideration. Singh (1967a) dwelt upon a multivariate expression of Murthy's (1964) product estimator. Further, the multi-auxiliary variables through a linear combination of single difference estimators were attempted by Raj (1965). In next bid of investigation Singh (1967b) extended the ratio-cum-product estimators to multi-supplementary variables. An innovative idea of weighted sum of single ratio and product estimators leading to multivariate was developed by Rao and Mudholkar (1967). Much versatile effort was made by John (1969) by considering a general ratio-type Estimator that, in turn, presented n unified class of estimators obtaing various particular estimators suggested by previous authors such as Olkin's (1958) and Singh's (1967a). Srivastava (1971) dealt with a general ratio-type estimator unifying previously developed estimators by eminent authors engaged in this area of investigation. Searls (1964) and Sisodia & Dwivedi (1981) used coefficient of variation of study and auxiliary variables respectively to estimate population mean of study variable. Srivenkataramana (1980) first proposed the dual to ratio estimator for estimating population mean. Kadilar and Cingi (2004, 2005) analyzed combinations of regression type estimators in the case of two auxiliary variables. In the same situation, Perri (2005) proposed some new estimators obtained from Singh's (1965, 1967b) ones. Singh and Tailor (2005), Tailor and Sharma (2009) worked on ratio-cum-product estimators. Sharma and Tailor (2010) proposed a ratio-cum-dual to ratio estimator for the estimation of finite population mean of the study variable y. In the series of improvement Das and
Improved Estimation of the Population Mean Using Known Parameters of an Auxiliary Variable
2011
An improved ratio-cum-product type estimator of the finite population mean is proposed using known information on the coefficient of variation of an auxiliary variate and correlation coefficient between a study variate and an auxiliary variate. Realistic conditions are obtained under which the proposed estimator is more efficient than the simple mean estimator, usual ratio and product estimators and estimators proposed by Singh and Diwivedi (
Some Modified Unbiased Estimators of Population Mean
The use of supplementary information on auxiliary variables in sample surveys was extensively discussed by Cochran and Jessen. In their work they showed that regression estimator is superior to the other estimators (viz. ratio and mean per unit estimators etc.).This paper proposes a new kind of estimator based on appropriate weighing of the sample means of the main and the auxiliary variables. It is shown that the proposed estimator is more efficient when compared with the regression, ratio and the mean per unit estimator under certain restrictions on the correlation coefficient between main and the auxiliary variables.
On Using the Conventional and Nonconventional Measures of the Auxiliary Variable for Mean Estimation
Mathematical Problems in Engineering, 2021
In this paper, we propose an improved new class of exponential-ratio-type estimators for estimating the finite population mean using the conventional and the nonconventional measures of the auxiliary variable. Expressions for the bias and MSE are obtained under large sample approximation. Both simulation and numerical studies are conducted to validate the theoretical findings. Use of the conventional and the nonconventional measures of the auxiliary variable is very common in survey research, but we observe that this does not add much value in many of the estimators except for our proposed class of estimators.
Some Improved Estimators of Population Mean Using Information on Two Auxiliary Attributes
In this paper, we have studied the problem of estimating the finite population mean when information on two auxiliary attributes are available. Some improved estimators in simple random sampling without replacement have been suggested and their properties are studied. The expressions of mean squared error's (MSE's) up to the first order of approximation are derived. An empirical study is carried out to judge the best estimator out of the suggested estimators.
Journal of Applied Mathematics, Statistics and Informatics, 2020
The present paper provides a remedy for improved estimation of population mean of a study variable, using the information related to an auxiliary variable in the situations under Simple Random Sampling Scheme. We suggest a new class of estimators of population mean and the Bias and MSE of the class are derived upto the first order of approximation. The least value of the MSE for the suggested class of estimators is also obtained for the optimum value of the characterizing scaler. The MSE has also been compared with the considered existing competing estimators both theoretically and empirically. The theoretical conditions for the increased efficiency of the proposed class, compared to the competing estimators, is verified using a natural population.