Regression Estimator With Triple Sampling The Double Non-Respondents

Subsampling the non-respondents introduced by Hansen-Hurwitz method is a very important method of dealing with response problem, it has been used in actual sample survey and analysis. Hansen-Hurwitz method has advantages, which delete missing data method, maximum likelihood method, interpolation method do not have, and is used more often.Subsampling the non-respondents introduced by Hansen-Hurwitz method can be traced back to the last century. Hansen and Hurwiz (1946) proposed a method to tackle non-respondents, we now call the proposed estimator for Hansen-Hurwitz estimator. Hansen and Hurwiz (1946) didn’t repeated investigation to get more information, but to extract a subsample of the non-respondents, and used the subsample’s information to representation the whole layer’s information. Cochran (1977) by using the method of Hanson-Hurwitz, proposed ratio and regression estimator of the population mean, he assumes that all individuals surveyed have auxiliary variable information that is known. Okafor and Lee (2000) considered circumstance when the auxiliary variable’s information is unknown,and conducted a preliminary sampling, through the preliminary sample make an estimate of the population mean of auxiliary variables, and then from the formal sampling estimated variables of interest, and gives the corresponding estimator.Then, uses Hansen-estimator to construct ratio estimators and regression estimators, because Hansen-Hurwitz estimator can more fully utilized the information has been obtained, the regression estimator can take advantage of auxiliary information to improve the accuracy of estimator.This article is based on previous studies, further discuss the population have double layer non-respondents:In the first, conduct a pre-condition to estimate the mean of the population as an auxiliary variable, then conduct formal investigation, but there are non-response in the sample, select a subsample randomly from these non-respondents of the investigation, there are non-respondents (second non-respondents) again, this is the second re-sampling. Select a subsample randomly from these second non-respondents and all sample of the second non-respondents response, this is the third re-sampling. Triple sampling the doublenon-response layer, and gives the corresponding Hansen-Hurwitz estimator, triple sample the double non-response layer and construct regression estimator, and gives the variance and variance estimator of the regression estimatorUnder the conditions of cost constraints, gives optimal design parameters. compare the relative efficiency of triple sample the double non-response regression estimator and triple sample the double non-response Hansen-Hurwitz estimator, and relative efficiency of triple sample the double non-response regression estimator and triple sample the double non-response ratio estimator.