S. K. YadavDepartment of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, Uttar Pradesh, IndiaSheela MisraDepartment of Statistics, University of Lucknow, Lucknow-226007, Uttar Pradesh, IndiaH. N. DhunganaDepartment of Community Medicine, Integral Institute of Medical Sciences and Research,Lucknow, Uttar Pradesh, IndiaS. S. MishraDepartment of Mathematics and Statistics (A Centre of Excellence) Dr RML Avadh University, Faizabad-224001, Uttar Pradesh, IndiaAbstract The present manuscript is a critical and chronological review of the ratio type
estimators of population mean of the study variable using auxiliary information on
a single auxiliary variable. In this paper various ratio type estimators of population
mean in the literature have been given chronologically. The large sample properties
that is biases and the mean squared errors of these ratio type estimators of population
mean have been given up to the first order of approximation. The expressions of the
bias and the mean squared error of every mentioned estimator have been given. The
optimum values of the characterizing scalars have been given for the generalized type
estimators having characterizing scalars and the minimum values of the mean squared
errors of corresponding estimators have been obtained for these optimum values of the
characterizing scalars. This work is believed to provide insightful gain in systematic
manner for the researchers who are engaged in the field to explore it through serious
investigation. 2010 Mathematics Subject Classification. 62D05 Keywords and phrases. Auxiliary variable, Parameter, Estimator, Bias, Mean
Squared Error, Efficiency. |

Jñānābha > Volume 48 (No1-2018) >