Tests in adaptive regression via the Kac-Rice formula

2013/08/14 by Jonathan Taylor, Taylor, Jonathan, Joshua R. Loftus +3 · 2 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Machine Learning and ELM #Methodology (stat.ME) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1308.3020

openalex publication_date 2013/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive an exact p-value for testing a global null hypothesis in a general adaptive regression problem. The general approach uses the Kac-Rice formula, as described in (Adler & Taylor 2007). The resulting formula is exact in finite samples, requiring only Gaussianity of the errors. We apply the formula to the lasso, group lasso, and principal components and matrix completion problems. In the case of the lasso, the new test relates closely to the recently proposed covariance test of Lockhart et al. (2013).

Citations

• Rejoinder to "Least angle regression" by Efron et al
• Augmented sparse principal component analysis for high dimensional data
• Validity of the expected Euler characteristic heuristic

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