Rounding probabilities: Maximum probability and minimum complexity multipliers
type: Item
instance of: scholarly article
title: Rounding probabilities: Maximum probability and minimum complexity multipliers
zbMATH Open document ID: 0974.60009
DOI: 10.1016/S0378-3758(99)00077-4
author: Max Happacher
author: Friedrich Pukelsheim
published in: Journal of Statistical Planning and Inference
publication date: 2001-05-08T00:00:00Z
review text: The aim of the paper is to study four multipliers that are used in multiplier techniques of rounding theory based on rounding functions. In order to make the discrepancy close to zero, a good choice of multiplier is essential. The paper defines the four multipliers and shows their asymptotic equivalence behaviour. Section 2 reviews the authors' earlier results on the so-called ``easy-to-calculate'' multipliers, and the exactly unbiased multiplier. Sections 3 and 4 introduce the maximum probability (to vanishing discrepancy) multiplier, and the minimum complexity multiplier (that minimizes the expectation of the absolute value of discrepancy). Section 5 is devoted to the asymptotic discrepancy distribution, and the final Section 6 strongly recommend the ``easy-to-calculate'' multiplier since, asymptotically, it bears also the qualities of the other three multipliers, i.e. it achieves unbiasedness, maximizes the probability of a vanishing discrepancy, and minimizes the complexity of the generic rounding algorithm.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 1436936
zbMATH Keywords: asymptotic shift
zbMATH Keywords: convolution
zbMATH Keywords: discrepancy
zbMATH Keywords: multiplier methods
zbMATH Keywords: roundoff error
zbMATH Keywords: stationary rounding functions
zbMATH Keywords: unimodality
MaRDI profile type: Publication
cites work: Q4885487
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full work available at URL: s0378-3758(99)00077-4
OpenAlex ID: W2043766215
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description: scientific article; zbMATH DE number 1436936