Modified Class of Estimator for Finite Population Mean Under Two-Phase Sampling Using Regression Estimation Approach

This study proposed modified a class of estimator in simple random sampling for the estimation of population mean of the study variable using as axillary information. The biases and MSE of suggested estimators were derived up to the first order approximation using Taylor’s series expansion approach. Theoretically, the suggested estimators were compared with the existing estimators in the literature. The mean square errors (MSE) and percentage relative efficiency (PRE) of proposed estimators and that of some existing estimators were computed numerically and the results revealed that the members of the proposed class of estimator were more efficient compared to their counterparts and can produce better estimates than other estimators considered in the study.

MODIFICATION OF SEPARATE RATIO TYPE EXPONENTIAL ESTIMATOR: A POST-STRATIFICATION APPROACH

In this research, modification of separate ratio type exponential estimator introduced in an earlier study is proposed. Expressions for the bias and mean square error (MSE) of the proposed estimator up to first degree of approximation are derived. The optimum value of the constant which minimize the MSE of the suggested estimator is also obtained. In the same vein, efficiency comparisons between the proposed estimator and some related existing ones under the case of post-stratification is conducted. Empirical studies have been conducted to demonstrate the efficiencies of the suggested estimators over other considered estimators. The proposed MSE and Percentage Relative Efficiency (PRE) were used to evaluate the achievement of the modified estimator.

Ameliorated Class of Estimators of Finite Population Variance

A class of ratio estimators of finite population variance is proposed in this study. The properties of the proposed estimators have been derived using Taylor’s Series method up to first order of approximation. The efficiency conditions which are the mean square errors (MSEs) and percentage relative efficiency (PRE) of the proposed estimators over existing estimators have been established. The analytical illustration was also conducted to affirm the theoretical results. The results of the empirical study revealed that the proposed estimators are more efficient than the existing estimators considered in the study.

A Note on the Performance of Biased Estimators with Autocorrelated Errors

It is a well-established fact in regression analysis that multicollinearity and autocorrelated errors have adverse effects on the properties of the least squares estimator. Huang and Yang (2015) and Chandra and Tyagi (2016) studied the PCTP estimator and the r-(k,d) class estimator, respectively, to deal with both problems simultaneously and compared their performances with the estimators obtained as their special cases. However, to the best of our knowledge, the performance of both estimators has not been compared so far. Hence, this paper is intended to compare the performance of these two estimators under mean squared error (MSE) matrix criterion. Further, a simulation study is conducted to evaluate superiority of the r-(k,d) class estimator over the PCTP estimator by means of percentage relative efficiency. Furthermore, two numerical examples have been given to illustrate the performance of the estimators.

Adapted Factor-Type Imputation Strategies

The present paper provides alternative improved Factor-Type (F-T) estimators of population mean in presence of item non-response for the practitioners. The proposed estimators have been shown to be more efficient than the four existing estimators which are more efficient than the usual ratio and the mean estimators. Optimum conditions for minimum mean squared error are obtained for the new estimators. Empirical comparisons based on three different data sets establish that the proposed estimators record least mean squared error and hence a substantial gain in Percentage Relative Efficiency (P.R.E.), over these five contemporary estimators.