Competitive On‐line Statistics

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.

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