Use of ranks in probability propoetional to size sampling

Abstract

Use of ranks in unequal probability sampling is examined for sample selection, stratification as well as determining the strata boundaries. A few sampling schemes are proposed and investigated, For samples of size two, two sampling schemes and their 1PPS versions are discussed, An extension of these schemes to general sample sizes is outlined. Nonnegative unbiased variance estimators are proposed in each case, An empirical comparison is included.

Keywords:

• Horvitz-Thompson estimator
• IPPS scheme
• PPS sampling
• ranks as size measure
• stratification
• Yates-Grundy variance estimator