Comparison of Various Estimators in Sampling through Monte-Carlo

Abstract

Generally, sample survey statistician i.e. faced with the problem as to how he should make the best use of available information on some auxiliary variable which is highly correlated with the variable under study. The types of population which we come across in surveys for estimating the production or extent of cultivation of agricultural commodities generally follow a linear regression relationship on auxiliary character X. Hence in this thesis the population was assumed to be coming from o bivariate normal distribution. Four populations were generated for four different values of ranging between 0.3 and 0.9 for given mean and given standard deviations. The X-observations were treated as auxiliary variates and y-observations were treated as study variated. The present study was aimed at finding out the suitable method of estimation when auxiliary variates are available. The study was carried out through Monte-Carlo methods which envisage the simulation of populations which have the given pattern of relationship between the study and auxiliary variates for some reasonably fixed values of parameters. From each on the generated population consisting of 200 units, corresponding to the four varying values of row, 200 independent samples (four sets of 50 each) for varying sample sizes were selected. Each of these samples provided estimates of population total by using three different methods of estimation along with the corresponding estimates of the variances. One estimate of the bias in the estimate of the population moon estimated through ratio and regression methods of estimation is provided by taking the difference between the average value of the estimates taken over 200 samples and the true value of the population mean. Similarly the mean square of 200 samples values of the estimates of the population mean provides estimate of the true value of variances of an estimate of a given parameter. The present study has revealed the following results. (I) So far as the amount of bias in estimating the population mean through ratio and regression estimator is concerned, the study has revealed that its value is appreciably small being less than 2% or the mean for all the population. (II) Comparing the performances of the ratio and regression methods of estimation with the sample mean for estimating the population mean on the basis of mean square errors it has been established that when i.e. of the order 0.3 or less than sample mean is preferable over the ratio and regression method of estimation since the true variance as estimated by the mean squares between the estimates of the population mean provided by 200 independent samples, is consistently smaller in the case of sample mean than in the case of either ratio or regression method of estimation. For the population – I even when the criterion row is smaller the Ox and Oy hold good the study has revealed that sample mean is superior than both ratio regression method of estimation.