Efficient Methods Of Estimation For Population Mean In Some Sampling Designs

In sample surveys,the problem of estimating population parameters is a common issue relating to the field of agriculture,economics,medicine and population studies.The literature on survey sampling describes a great variety of techniques for utilizing information on auxiliary variates by ratio,product and regression methods of estimation to estimate the population parameters such as the mean and variance of a variate under study.Ratio estimators may be used to estimate the ratios like per capita income or expenditure,proportion of expenditure on different items,proportion of unemployed persons,sex ratio,birth rate,death rate,yield per unit area and the use of fertilizer/pesticides per hectare for a particular crop etc.The aim of this thesis is to propose efficient generalized forms of ratio-type estimators for the estimation of finite population mean under different scenarios discussed one by one as below.Supplementary information provided by an auxiliary or subsidiary variable enhances the precision of the estimators of the population parameters.Several estimators have been developed in this context.A limited work is found on the estimation of parameters through median of an auxiliary variable and through the correlation coefficient between study and auxiliary variable.Moving along this direction,Yadav et al.(2014a)proposed only two ratio-type estimators utilizing median and Kadilar and Cingi(2006a)proposed only four ratio-type estimators using correlation coefficient.There is need to extend their work to develop more flexible and efficient forms.Therefore,in this thesis we proposed an optimal generalized form of ratio-type estimators based on median of an auxiliary variable and another flexible form based on known correlation coefficient.Most of the estimators in literature used conventional measures of the auxiliary variable such as mean,standard deviation,coefficient of variation,coefficient of skewness and coefficient of kurtosis to improve the efficiency of the estimators.Here comes a new idea to check whether the non-conventional measures of an auxiliary variable like quartile deviation,mid-range,inter-quartile range,quartile average,tri-mean and Hodge-Lehmann estimator etc.can do the same.To meet this challenge,we developed an optimal family of estimators for population mean using conventional and non-conventional measures of an auxiliary variable.Haq et al.(2017)proposed an estimator in simple random sampling based on the fact that when there exists a sufficient amount of correlation between the study variable and auxiliary variable,the ranks of the auxiliary variable are also correlated with the values of the study variable.Thtus,the ranked auxiliary variable may help to increase the efficiency of the estimators.There is necessity to outspread their work in stratified random sampling as it provides more precise estimators in planning survey.Therefore,we suggested new improved estimators based on dual auxiliary information in simple as well as in stratified random sampling.Continuing our work,we explored a new optimal class of estimators for estimating population mean by combining three concepts:1)information on auxiliary variable 2)the ranks of auxiliary variable and 3)Hartley-Ross type unbiased estimation.This idea is novel in the way that the previous work deals them separately but we combine them together.Traditional estimation based on the assumptions:1)there is a complete response and 2)recorded information from individuals is correct but in practice it is not always true.Considering this practical situation of non-response and measurement errors jointly,we proposed an optimum generalized form for estimating population mean using conventional and non-conventional measures of an auxiliary variable under simple random sampling that can generate a large number of estimators.The mathematical expressions of bias,mean squared error(MSE)and minimum MSE of all the proposed estimators are derived up to first order of approximation.Illustrative examples drawn from,various fields of application such as agriculture,business management,demography,economics,education,engineering,industry,medical sciences,social sciences etc.are taken to highlight the potential of the proposed estimators over the existing estimators cover in this thesis.In addition,we have investigated and compared the performance of the proposed generalized forms using Monte Carlo simulation study.A comprehensive review and perspective of the well-known existing estimators for enhanced estimation of population mean is also provided in this thesis.The theoretical and numerical findings of this thesis indicate that all the proposed estimators are more efficient for estimating population mean under different situations.Moreover,proposed generalized forms are flexible enough that many existing estimators are proved to be their members.Therefore,it is helpful recommendation to the researchers that all the proposed estimators may be used for future applications.