Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function

DOI10.1214/009053604000000896zbMath1065.62109arXivmath/0504509OpenAlexW4299585263MaRDI QIDQ1781158

Béatrice Laurent, Sylvie Huet, Yannick Baraud

Publication date: 23 June 2005

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504509

zbMATH Keywords

Gaussian regressionrate of testingtest of convexitytest of monotonicitytest of positivitytests of qualitative hypotheses

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Hypothesis testing in multivariate analysis (62H15) General nonlinear regression (62J02)

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Cites Work

• Unnamed Item
• Asymptotically minimax hypothesis testing for nonparametric alternatives. I
• Adaptive tests of linear hypotheses by model selection
• Testing for monotonicity of a regression mean by calibrating for linear functions.
• Testing monotonicity of regression.
• Multiscale testing of qualitative hypotheses
• On nonparametric tests of positivity/monotonicity/convexity
• Adaptive tests of qualitative hypotheses
• Tests for monotonicity of a regression mean with guaranteed level
• An alternative point of view on Lepski's method