ON-LINE PREDICTIVE LINEAR REGRESSION
成果类型：
Article
署名作者：
Vovk, Vladimir; Nouretdinov, Ilia; Gammerman, Alex
署名单位：
University of London; Royal Holloway University London
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/08-AOS622
发表日期：
2009
页码：
1566-1590
关键词：
摘要：
We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard treatment of prediction in linear regression analysis has two drawbacks: (1) the classical prediction intervals guarantee that the probability of error is equal to the nominal significance level epsilon, but this property per se does not imply that the long-run frequency of error is close to epsilon; (2) it is not suitable for prediction of complex systems as it assumes that the number of observations exceeds the number of parameters. We state a general result showing that in the on-line protocol the frequency of error for the classical prediction intervals does equal the nominal significance level, up to statistical fluctuations. We also describe alternative regression models in which informative prediction intervals can be found before the number of observations exceeds the number of parameters. One of these models, which only assumes that the observations are independent and identically distributed, is popular in machine learning but greatly underused in the statistical theory of regression.
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