Permutational Extreme Values of Autocorrelation Coefficients and a Pitman Test Against Serial Dependence

Normal approximations, as provided by permutational central limit theorems, conditionally can be arbitrarily bad. Such approximations therefore are poorly suited to the construction of critical values for Pitman (permutation) tests. A classical remedy consists in substituting a beta approximation (o...

Full description

Saved in:
Bibliographic Details
Published in:The Annals of statistics 1992-03, Vol.20 (1), p.523-534
Main Authors: Hallin, Marc, Melard, Guy, Milhaud, Xavier
Format: Article
Language:English
Subjects:
05C38
62G10
62M10
Approximation
Autocorrelation
Business orders
Central limit theorem
Correlation coefficients
Correlations
Critical values
Exact sciences and technology
Mathematical functions
Mathematical permutation
Mathematics
Nonparametric inference
Permutation tests
Pitman tests
Probability and statistics
Sciences and techniques of general use
serial correlation
Statistics
the travelling salesman problem
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Normal approximations, as provided by permutational central limit theorems, conditionally can be arbitrarily bad. Such approximations therefore are poorly suited to the construction of critical values for Pitman (permutation) tests. A classical remedy consists in substituting a beta approximation (over the appropriate conditional interval range) for the normal one. Whereas deriving permutational extreme values for usual, nonserial statistics is generally straightforward, the corresponding problem for serial statistics (e.g., autocorrelation coefficients), however, appears somewhat more difficult. This problem, which is shown to reduce to a particular case of the well-known travelling salesman problem, is explicitly solved here for the autocorrelation coefficient of order one, allowing for a simple computation of permutational critical values for Pitman tests against serial dependence. The case of higher order autocorrelations is, however, of a different nature and requires another approach.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1176348536