Best invariant and minimax estimation of quantiles in finite populations

Yaakov Malinovsky*, Yosef Rinott

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The theoretical literature on quantile and distribution function estimation in infinite populations is very rich, and invariance plays an important role in these studies. This is not the case for the commonly occurring problem of estimation of quantiles in finite populations. The latter is more complicated and interesting because an optimal strategy consists not only of an estimator, but also of a sampling design, and the estimator may depend on the design and on the labels of sampled individuals, whereas in iid sampling, design issues and labels do not exist. We study the estimation of finite population quantiles, with emphasis on estimators that are invariant under the group of monotone transformations of the data, and suitable invariant loss functions. Invariance under the finite group of permutation of the sample is also considered. We discuss nonrandomized and randomized estimators, best invariant and minimax estimators, and sampling strategies relative to different classes. Invariant loss functions and estimators in finite population sampling have a nonparametric flavor, and various natural combinatorial questions and tools arise as a result.

Original languageEnglish
Pages (from-to)2633-2644
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume141
Issue number8
DOIs
StatePublished - Aug 2011

Keywords

  • Behavioral and randomized estimators
  • Loss functions
  • Median
  • Monotone transformations
  • Sampling and estimation strategies
  • Simple random sample

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