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May 2016 Greedy algorithms for prediction
Alessio Sancetta
Bernoulli 22(2): 1227-1277 (May 2016). DOI: 10.3150/14-BEJ691


In many prediction problems, it is not uncommon that the number of variables used to construct a forecast is of the same order of magnitude as the sample size, if not larger. We then face the problem of constructing a prediction in the presence of potentially large estimation error. Control of the estimation error is either achieved by selecting variables or combining all the variables in some special way. This paper considers greedy algorithms to solve this problem. It is shown that the resulting estimators are consistent under weak conditions. In particular, the derived rates of convergence are either minimax or improve on the ones given in the literature allowing for dependence and unbounded regressors. Some versions of the algorithms provide fast solution to problems such as Lasso.


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Alessio Sancetta. "Greedy algorithms for prediction." Bernoulli 22 (2) 1227 - 1277, May 2016.


Received: 1 August 2013; Revised: 1 December 2014; Published: May 2016
First available in Project Euclid: 9 November 2015

zbMATH: 06562310
MathSciNet: MR3449813
Digital Object Identifier: 10.3150/14-BEJ691

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability


Vol.22 • No. 2 • May 2016
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