The Annals of Statistics

On Karlin's Conjecture for Random Replacement Sampling Plans

O. Krafft and M. Schaefer

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Abstract

In 1974 Karlin introduced the concept of random replacement schemes and conjectured that the componentwise monotonicity of the replacement probabilities (condition A) is equivalent to a corresponding ordering of expectations of all functions $\phi$ from a certain class $\mathscr{C}_K$ (condition B). In this paper it is shown that A implies B for sample sizes $n \leq 5$ and--provided the sample space is sufficiently large--also for $n \geq 6$. By a counterexample it is shown that $\mathscr{C}_K$ is not suitable for A being implied by B, i.e. one direction of Karlin's conjecture is disproved.

Article information

Source
Ann. Statist., Volume 12, Number 4 (1984), 1528-1535.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346809

Digital Object Identifier
doi:10.1214/aos/1176346809

Mathematical Reviews number (MathSciNet)
MR760705

Zentralblatt MATH identifier
0598.62010

JSTOR
links.jstor.org

Subjects
Primary: 62D05: Sampling theory, sample surveys
Secondary: 60G05: Foundations of stochastic processes 05A20: Combinatorial inequalities

Keywords
Random replacement sampling plans combinatorial inequalities partial ordering

Citation

Krafft, O.; Schaefer, M. On Karlin's Conjecture for Random Replacement Sampling Plans. Ann. Statist. 12 (1984), no. 4, 1528--1535. doi:10.1214/aos/1176346809. https://projecteuclid.org/euclid.aos/1176346809


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