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2018 | OriginalPaper | Buchkapitel

10. Analysis of High-Dimensional Regression Models Using Orthogonal Greedy Algorithms

verfasst von : Hsiang-Ling Hsu, Ching-Kang Ing, Tze Leung Lai

Erschienen in: Handbook of Big Data Analytics

Verlag: Springer International Publishing

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Abstract

We begin by reviewing recent results of Ing and Lai (Stat Sin 21:1473–1513, 2011) on the statistical properties of the orthogonal greedy algorithm (OGA) in high-dimensional sparse regression models with independent observations. In particular, when the regression coefficients are absolutely summable, the conditional mean squared prediction error and the empirical norm of OGA derived by Ing and Lai (Stat Sin 21:1473–1513, 2011) are introduced. We then explore the performance of OGA under more general sparsity conditions. Finally, we obtain the convergence rate of OGA in high-dimensional time series models, and illustrate the advantage of our results compared to those established for Lasso by Basu and Michailidis (Ann Stat 43:1535–1567, 2015) and Wu and Wu (Electron J Stat 10:352–379, 2016).

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Vorheriges Kapitel High-Dimensional Classification

Nächstes Kapitel Semi-supervised Smoothing for Large Data Problems

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Titel: Analysis of High-Dimensional Regression Models Using Orthogonal Greedy Algorithms
verfasst von: Hsiang-Ling Hsu
Ching-Kang Ing
Tze Leung Lai
Verlag: Springer International Publishing
Buch: Handbook of Big Data Analytics
Print ISBN: 978-3-319-18283-4

Electronic ISBN: 978-3-319-18284-1

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-18284-1_10

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