In this paper generalized classes of modified ratio type and regression-cum-ratio type estimators of the finite population mean of the study variable are suggested in the presence of two auxiliary variables in simple random sampling without replacement when the population means of the auxiliary variables are known in advance. Some special cases of the generalized estimators are compared with respect to their biases and efficiencies both theoretically and with the help of some natural populations.
This paper presents a family of dual to ratio-cum-product estimators for the finite population mean. Under simple random sampling without replacement (SRSWOR) scheme, expressions of the bias and mean-squared error (MSE) up to the first order of approximation are derived. We show that the proposed family is more efficient than usual unbiased estimator, ratio estimator, product estimator, Singh estimator (1967), Srivenkataramana (1980) and Bandyopadhyaya estimator (1980) and Singh et al. (2005) estimator. An empirical study is carried out to illustrate the performance of the constructed estimator over others.
Since the quadratic finite population functions can be expressed as totals over a synthetic population consisting of some ordered pairs of elements of the initial population, the traditional and penalized calibration technique is used to derive some calibrated estimators of the quadratic finite population functions. A linear combination of estimators discussed is considered as well. A comparison of approximate variances of the calibrated estimators is also presented. A simulation study is performed to analyze the empirical properties of the calibrated estimators of the finite population variance and covariance which appear as special cases of the quadratic functions. It is shown also how the calibrated estimators of the population covariance (variance) can be applied in regression estimation of the finite population total.
Many dual frame estimators have been proposed in the statistics literature. Some of these estimators are theoretically optimal but hard to apply in practice, whereas others are applicable but have larger variances than the first group. In this paper, a Joint Calibration Estimator (JCE) is proposed that is simple to apply in practice and meets many desirable properties for dual frame estimators. The JCE is asymptotically design unbiased conditional on the strong relationship between the estimation variable and the auxiliary variables employed in the calibration. The JCE achieves better performance when the auxiliary variables can fully explain the variability in the study variables or at least when the auxiliary variables are strong correlates of the estimation variables. As opposed to the standard dual frame estimators, the JCE does not require domain membership information. Even if included in the JCE auxiliary variables, the effect of the randomly misclassified domains does not exceed the random measurement error effect. Therefore, the JCE tends to be robust for the misclassified domains if included in the auxiliary variables. Meanwhile, the misclassified domains can significantly affect the unbiasedness of the standard dual frame estimators as proved theoretically and empirically in this paper.
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