Competitive on-line statistics (1999)
| Venue: | International Statistical Review |
| Citations: | 96 - 15 self |
BibTeX
@ARTICLE{Vovk99competitiveon-line,
author = {Volodya Vovk},
title = {Competitive on-line statistics},
journal = {International Statistical Review},
year = {1999},
volume = {69},
pages = {2001}
}
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Abstract
A radically new approach to statistical modelling, which combines mathematical techniques of Bayesian statistics with the philosophy of the theory of competitive on-line algorithms, has arisen over the last decade in computer science (to a large degree, under the influence of Dawid’s prequential statistics). In this approach, which we call “competitive on-line statistics”, it is not assumed that data are generated by some stochastic mechanism; the bounds derived for the performance of competitive on-line statistical procedures are guaranteed to hold (and not just hold with high probability or on the average). This paper reviews some results in this area; the new material in it includes the proofs for the performance of the Aggregating Algorithm in the problem of linear regression with square loss. Keywords: Bayes’s rule, competitive on-line algorithms, linear regression, prequential statistics, worst-case analysis.
Keyphrases
competitive on-line statistic competitive on-line algorithm linear regression prequential statistic stochastic mechanism worst-case analysis computer science large degree bayes rule mathematical technique new approach last decade competitive on-line statistical procedure aggregating algorithm new material high probability bayesian statistic square loss statistical modelling
