| Abstract: | ABSTRACT The systematic sampling (SYS) design (Madow and Madow, 1944
Madow , L. H. ,
Madow , W. G. ( 1944 ). On the theory of systematic sampling . Ann. Math. Statist. 15 : 1 – 24 .Crossref] , Google Scholar]) is widely used by statistical offices due to its simplicity and efficiency (e.g., Iachan, 1982
Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .Crossref], Web of Science ®] , Google Scholar]). But it suffers from a serious defect, namely, that it is impossible to unbiasedly estimate the sampling variance (Iachan, 1982
Iachan , R. ( 1982 ). Systematic sampling a critical review . Int. Statist. Rev. 50 : 293 – 303 .Crossref], Web of Science ®] , Google Scholar]) and usual variance estimators (Yates and Grundy, 1953
Yates , F. ,
Grundy , P. M. ( 1953 ). Selection without replacement from within strata with probability proportional to size . J. Roy. Statist. Soc. Series B 1 : 253 – 261 . Google Scholar]) are inadequate and can overestimate the variance significantly (Särndal et al., 1992
Särndal , C. E. ,
Swenson , B. ,
Wretman , J. H. ( 1992 ). Model Assisted Survey Sampling . New York : Springer-Verlag , Ch. 3 .Crossref] , Google Scholar]). We propose a novel variance estimator which is less biased and that can be implemented with any given population order. We will justify this estimator theoretically and with a Monte Carlo simulation study. |
