Stochastic Comparisons of Symmetric Sampling Designs

Larry Goldstein, Yosef Rinott, Marco Scarsini*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We compare estimators of the integral of a monotone function f that can be observed only at a sample of points in its domain, possibly with error. Most of the standard literature considers sampling designs ordered by refinements and compares them in terms of mean square error or, as in Goldstein et al. (2011), the stronger convex order. In this paper we compare sampling designs in the convex order without using partition refinements. Instead we order two sampling designs based on partitions of the sample space, where a fixed number of points is allocated at random to each partition element. We show that if the two random vectors whose components correspond to the number allocated to each partition element are ordered by stochastic majorization, then the corresponding estimators are likewise convexly ordered. If the function f is not monotone, then we show that the convex order comparison does not hold in general, but a weaker variance comparison does.

Original languageEnglish
Pages (from-to)407-420
Number of pages14
JournalMethodology and Computing in Applied Probability
Volume14
Issue number3
DOIs
StatePublished - Sep 2012

Keywords

  • Convex order
  • Exchangeable partitions of integers
  • Stochastic majorization
  • Stratified sampling

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