STUDY OF MISSING VALUES UNDER DIFFEREA'J"T IMPUTATION METHODS

Abstract

In t his research, we suggest different families of estimators for t he imputation of missing complete at random (MCAR) values for t he estimation of finite popul ation mean (?) and total (2: Y) of the study variable (y) under different sampling schemes. The known population parameters of the auxiliary variable such as: mean (X), ranks (R.(c,,) ), truncated mean (\I), variance (S~ , coeffi cient of variation (ex), coefficient of kurtosis (,B2(x) ) and correlation coefficient (Pyx ) have been used to estimate t he parameters of interest more precisely. Mathematical expressions for bia::; and mean square errors of resultant estimators are obtaiued up to first order of approximation. For the con'lparative comparison, theoretical conditions are also defined by which t he proposed imputation procedures performs better than their counterparts. For the numerical comparison of the proposed procedures with existing ones is performed using Monte Carlo experiment by generating hypothetical population and real life data sets by repeating t he process ) times at varying response rate. A gelleralized families of ratio awl difference type estimators arc proposed for handling the non-response bias by utilizing t he ranks of the auxiliary variable under SRS. On the basis of numerical results, we easily understand that, our proposed families of estimators can perform much better as compared to traditional ones. A modified class of ratio type estimators is suggested for imputing the MCAR values by using the higher order moments of the auxiliary variable. The suggested imputation procedure for estimating finite population mean dominates over the other competitor estimators at varying response rate. The idea of truncating the auxiliary information is also reported in this research for estimating the missing va.lues in a significant way. A class of ratio-exponential type estimators is proposed to impute t he missing value by using the truncated auxiliary variable (v) and the V11 Abstract Vlll ranks of the auxili ary variables (1'(x» )' The proposed class of estimators is perform beLter as compared to their counterpart. vVe support our results through two real life data sets at the response rate between 20% to 80%. Under the comparative measures, when Lhe observation units are varying in size and we have no auxili ary informatioll in hand . A mixture of two phase and pps sampling scheme is proposed by combine their features. A class of estimators is reformulated with four possible situations of non-response in the study variable or/alld the auxiliary variable under proposed sampling scheme. A comprehensive numerical comparison in terms of PRE is additionally consider at varying response rate for each of the pre-characterized circumstances. The imputation of non-response in RSS is considered by modifying existing family of estimators. Theoretical results for bias and mean square errors are also reported up to first order of approximation. The relative comparison between different proposed and existillg illlput.ation strategies is dcfilled through the silllulatioll and real life data sets. The simulation study of the modifi ed procedures is carried by generating the random number from the two hypothetical population , (i) a population is generated from normal distribution with mean (J.L ) an d variance (0'2) and (ii) the other population is generate from the exponential distribution with mean (..\) at distinct parametric values. The suggested imputation mechanism perform better as compared to conventional mechanisms. In last few decades, the utilization of rayv rnomellt for t he estimation of fillite population parameters has got suustantial R.ttcntion in the field of survey sR.mpling. vVc define an imputation strategy by using the raw moments of t he auxiliary variable for filling t he item non-response. A r atio-exponential type family of estimators is defin ed with the significant lise of t he auxiliary inforlllation. To !:; uppOl't t he relative performance, four dift'crent real life populations are studied along with simulated data sets by generating the random population from: (i) bivariate normal distribution with means (J.Lx and J.Ly) and variances (0'; and 0';) and (ii) the second population is generated from gamma distribution with parameters (a and b). The small area predictive estimation of population total is also illustrated for the case of known and unknown domain/area membership (DJ Three popula tion models says: (i) Homogeneous population model (HPM) , (ii) Ratio population Abstract ix m.odel (RPM) , and (iii) Linear population model (LPM) are used to defined the different estimators for the imputation of non-response. For the case of known and unknown area membership, two distinct real life data sets are used for the predictive estimation population total CL: y). The ranks of the auxiliary variable (w) are utilized productively to define the new population model for handling the non-response bias. From the reported results, we easily understand that new illlPutation population model arc lllorC efficicnt as cOlllpared to traditional model.