
Accession Number : AD0680438
Title : GENERALIZATION OF RATIO ESTIMATE FOR POPULATION TOTAL,
Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
Personal Author(s) : Walsh,John E.
Report Date : 01 OCT 1968
Pagination or Media Count : 16
Abstract : It is desired to estimate the total Y for a finite population (of size N) with unknown values. A population with corresponding known values is available. Also, a simple random sample of size n is taken from the unknown population. Let y bar be the mean of the sample while x bar is the mean of the n values from the known population that correspond to these sample values. The ratio estimate of Y is generalized to the form N(X bar)(y bar)/(A(x bar)+(1A)(X bar)), where X bar is the mean of the known population. Use of A = A sub o suitably chosen, yields an estimate that approximately is unbiased and has as small a variance as is attainable for a linear regression estimate. When A sub o is unknown in advance, it can be estimated (denoted by A' sub o). An estimate is developed for the standard deviation of the estimate using A' sub o. Also, an estimate is obtained for the standard deviation of this estimate for the standard deviation. Finally, some comparisons are made with the linear regression estimate. (Author)
Descriptors : (*SAMPLING, *DECISION THEORY), REGRESSION ANALYSIS, POPULATION(MATHEMATICS), ANALYSIS OF VARIANCE
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE