Bernoulli

  • Bernoulli
  • Volume 21, Number 4 (2015), 2484-2512.

Size-biased permutation of a finite sequence with independent and identically distributed terms

Jim Pitman and Ngoc M. Tran

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Abstract

This paper focuses on the size-biased permutation of $n$ independent and identically distributed (i.i.d.) positive random variables. This is a finite dimensional analogue of the size-biased permutation of ranked jumps of a subordinator studied in Perman–Pitman–Yor (PPY) [ Probab. Theory Related Fields 92 (1992) 21–39], as well as a special form of induced order statistics [ Bull. Inst. Internat. Statist. 45 (1973) 295–300; Ann. Statist. 2 (1974) 1034–1039]. This intersection grants us different tools for deriving distributional properties. Their comparisons lead to new results, as well as simpler proofs of existing ones. Our main contribution, Theorem 25 in Section 6, describes the asymptotic distribution of the last few terms in a finite i.i.d. size-biased permutation via a Poisson coupling with its few smallest order statistics.

Article information

Source
Bernoulli, Volume 21, Number 4 (2015), 2484-2512.

Dates
Received: October 2012
Revised: March 2014
First available in Project Euclid: 5 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1438777602

Digital Object Identifier
doi:10.3150/14-BEJ652

Mathematical Reviews number (MathSciNet)
MR3378475

Zentralblatt MATH identifier
1362.60036

Keywords
induced order statistics Kingman paint box Poisson–Dirichlet size-biased permutation subordinator

Citation

Pitman, Jim; Tran, Ngoc M. Size-biased permutation of a finite sequence with independent and identically distributed terms. Bernoulli 21 (2015), no. 4, 2484--2512. doi:10.3150/14-BEJ652. https://projecteuclid.org/euclid.bj/1438777602


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