The Use of a Ratio Estimate in Successive Sampling

SUMMARY A task faced annually by the Canadian Wildlife Service is to obtain reliable estimates of the number of birds killed during the hunting season. Estimates are published for zones within each province (usually two zones). The information is obtained from the National Harvest Survey through a mail questionnaire sent to a stratified random sample of hunters selected from the list of Federal Migratory Game Bird Hunting Permit holders with ecological zones as strata. Because of high variability in kill among hunters it has been a difficult problem to obtain reliable estimates within available resources. Successive sampling has been discussed in some detail by Jessen (1942), Patterson (1950), Yates (1960), Cochran (1963), Hansen et al. (1953), Sen (1971) and others. Their discussions have, however, been confined to combining a regression estimate from the matched portion of the sample with a mean per unit estimate based on the current occasion. Because in many surveys with several levels of stratification computations involving regression estimates become relatively complex, we propose to investigate in this paper some theory of successive sampling using a ratio estimate and examine the efficiency of a simpler estimate obtained by giving equal weights to the estimates based on the matched and unmatched portions.