Reconciliation of asymptotics for unequal probability sampling without replacement

Mohammad Ashraf Chaudhary, Pranab Kumar Sen

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In simple random sampling without replacement (SRSWOR), certain reverse martingale structures render simple asymptotics for the conventional linear statistics. In unequal probability sampling (UPS) WOR, such martingale-based methodology may not be generally adoptable. General asymptotics for UPSWOR sampling schemes, developed by Hartley and Rao (Ann. Math. Statist. 33 (1962) 350), and Hájek (Ann. Math. Statist. 35 (1964) 1491), rest on different sets of regularity assumptions, and they differ in their treatise too. Some anomalies in this context are eliminated here with a reconciliation of both the approaches, and estimation of the asymptotic variance of linear estimators is considered in the same vein. Applications to small area sampling are also stressed.

Original languageEnglish (US)
Pages (from-to)71-81
Number of pages11
JournalJournal of Statistical Planning and Inference
Issue number1
StatePublished - Mar 1 2002


  • Finite population correction
  • Horvitz-Thompson estimator
  • Inclusion probabilities
  • Poisson sampling scheme
  • Rejective sampling
  • Successive sampling
  • Variance estimators

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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