Distribution-free tests for polynomial regression based on simplicial depth

DOI10.1016/j.jmva.2008.06.009zbMath1163.62036OpenAlexW2049157520MaRDI QIDQ1002345

Robin Wellmann, Peter Harmand, Christine H. Müller

Publication date: 25 February 2009

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2008.06.009

zbMATH Keywords

polynomial regressionspectral decompositionsimplicial depthdistribution-free testsregression depthdegenerated U-statisticoutlier robustness

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Linear regression; mixed models (62J05) Nonparametric estimation (62G05) Generalized linear models (logistic models) (62J12)

Related Items (10)

Depth notions for orthogonal regression ⋮ Simple powerful robust tests based on sign depth ⋮ Data depth for simple orthogonal regression with application to crack orientation ⋮ Consistency and robustness of tests and estimators based on depth ⋮ Analysis of crack growth with robust, distribution-free estimators and tests for non-stationary autoregressive processes ⋮ New robust tests for the parameters of the Weibull distribution for complete and censored data ⋮ K-sign depth: from asymptotics to efficient implementation ⋮ Tests for multiple regression based on simplicial depth ⋮ Tests Based on Simplicial Depth for AR(1) Models With Explosion ⋮ Simplified simplicial depth for regression and autoregressive growth processes

Cites Work

• Depth estimators and tests based on the likelihood principle with application to regression
• Multivariate dispersion, central regions and depth. The lift zonoid approach
• On a notion of data depth based on random simplices
• Calculation of simplicial depth estimators for polynomial regression with applications
• Limit theorems for the simplicial depth
• Asymptotic distributions of the maximal depth estimators for regression and multivariate location
• The deepest regression method
• Estimators related to \(U\)-processes with applications to multivariate medians: Asymptotic normality
• General notions of statistical depth function.
• Structural properties and convergence results for contours of sample statistical depth functions.
• On depth and deep points: A calculus.
• On a notion of simplicial depth
• Regression Depth
• Location–Scale Depth
• A Quality Index Based on Data Depth and Multivariate Rank Tests
• A Distribution-Free Test for Regression Parameters
• Measuring overlap in binary regression.
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