Double Sampling With Subsampling The Non-respondents

The problem of nonresponse is very common when conducting a sample survey in the field of social sciences, agriculture and medical sciences. It often leads to nonresponse bias. Nonresponse bias is not only related with nonresponse rate, but also related with response probability. The best way to deal with nonresponse is to prevent it. The technique of improving response rate and response probability in survey design is proved having effect in reducing nonresponse bias. Scholars have done lots of work in dealing with nonresponse and get a lot of achievements. The most frequently used procedures to deal with item nonresponse is imputing methods. There are lots of good literatures on it up to now.For unit nonresponse, Hansen and Hurwitz (1946) first proposed subsampling the non-respondents and using double sampling for stratification to estimate the population mean or population total.This dissertation discusses the relationship between nonresponse rate and nonresponse bias. Our attention focus on double sampling adjustment, taking different estimates procedures and auxiliary information into account.At last, the empirical study will give some simulates about the relative efficiencies of two classes of double sampling estimators for population mean using auxiliary character in presence of nonresponse proposed by Khare, Pandey and Srivastava (2011)with respect to Hansen and Hurwitz estimator, and compare with other estimators for adjusting nonresponse proposed by Khare and Srivastava (1993) and Khare (1992). When using the sample value, the MSE of the two class estimator will lose some precision and consequently the two class estimator can’t maintain its superiority. For this reason, the major factor influence the MSE is discussed. When the nonresponse is MAR, the factor influence the two class of estimator is different, for the first class of double sampling estimator for population mean, the estimator of the covariance between object variable and auxiliary variable in non-respondents do affect the MSE, while the estimator of object variable affect the second class of double sampling estimator’s MSE. When the nonresponse is NMAR, the factor is the same, the estimator of the covariance between object variable and auxiliary variable in the population make the MSE of the two classes of double sampling estimators larger.