Estimating Variance of the Sample Mean in Two-phase Sampling with Unit Non-response Effect

In sample surveys, we always deal with two types of errors: Sampling error and non-sampling error. One of the most common non-sampling errors is nonresponse. This error happens when some sample units are not observed or viewed but they do not answer some of the questions. The complete prevention of this error is not possible, but it can be significantly reduced. The non-response causes bias and inflation of variance of estimators, so it reduces the precision of survey statistics. There are two types of non-response, unit non-response and item nonresponse. Different methods have been introduced for adjusting the effect of each of them. Weighting adjustment and imputation are two ways of adjusting the nonresponse effect of collecting data. A weighting is used to adjust the unit non-response effect and imputation is applied to adjust the item non-response effect. There are several designs that can be used to sample them. The proposed sampling design in this paper is a stratified two-phase sampling scheme that has been categorized as non-response. The purpose is estimating variance of the sample mean estimator in this sampling design by using the Jackknife estimation variance method. also in a simulation study, jackknife variance estimators for two estimators of the introduced four estimators (third and fourth) are calculated and compared based on relative efficiency and coefficients of variation. The data set used in this simulation study is data from Household Income and Expenditure survey conducted by statistical center of Iran in 1394.