Oracle inequalities for sign constrained generalized linear models

Yuta Koike, Yuta Tanoue

Research output: Contribution to journalArticle

Abstract

High-dimensional data have recently been analyzed because of advancements in data collection technology. Although many methods have been developed for sparse recovery in the past 20 years, most of these methods require the selection of tuning parameters. This requirement means that the results obtained with these methods heavily depend on tuning. Theoretical properties are developed for sign-constrained generalized linear models with convex loss function, which is one of the sparse regression methods that does not require tuning parameters. Recent studies on this subject have shown that, in the case of linear regression, sign-constraints alone could be as efficient as the oracle method if the design matrix enjoys a suitable assumption in addition to a traditional compatibility condition. This type of result is generalized to a model that encompasses logistic and quantile regressions. Some numerical experiments are performed to confirm the theoretical findings.

Original languageEnglish
JournalEconometrics and Statistics
DOIs
Publication statusPublished - 2019 Jan 1
Externally publishedYes

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Keywords

  • High-dimensions
  • Oracle inequality
  • Sign-constraints
  • Sparsity

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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