Validation of linear regression models

DOI10.1214/aos/1028144860zbMath0930.62041OpenAlexW2011931375MaRDI QIDQ1807092

Axel Munk, Dette, Holger

Publication date: 9 November 1999

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

Full work available at URL: https://doi.org/10.1214/aos/1028144860

zbMATH Keywords

equivalence of regression functionsvalidation of goodness of fitL2-distancenonparametric model check

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)

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Cites Work

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• Bandwidth choice for nonparametric regression
• A central limit theorem for \(m\)-dependent random variables
• Semiparametric comparison of regression curves
• An omnibus test for departures from constant mean
• Testing linear regression function adequacy without replication
• Testing the (parametric) null model hypothesis in (semiparametric) partial and generalized spline models
• Testing goodness-of-fit in regression via order selection criteria
• A simple goodness-of-fit test for linear models under a random design assumption
• Comparing nonparametric versus parametric regression fits
• A nonparametric test for the regression function: Asymptotic theory
• Nonparametric model checks for regression
• Testing precise hypotheses. With comments and a rejoinder by the authors
• Testing the equality of nonparametric regression curves
• Testing the Goodness of Fit of a Linear Model Via Nonparametric Regression Techniques
• On variance estimation in nonparametric regression
• The Use of Marginal Likelihood for a Diagnostic Test for the Goodness of Fit of the Simple Linear Regression Model
• Residual variance and residual pattern in nonlinear regression
• Testing lack of fit in regression without replication
• The choice of approximative models in nonlinear regression
• Comparison of Different Methods for Decision-Making in Bioequivalence Assessment
• Diagnostics for Assessing Regression Models
• Regression Model Diagnostics
• General Estimates of the Intrinsic Variability of Data in Nonlinear Regression Models
• Estimating the Variance In Nonparametric Regression—What is a Reasonable Choice?
• Test for the choice of approximative models in nonlinear regression when the variance is unknown
• Designs for Regression Problems with Correlated Errors III
• Bootstrap Test for Difference Between Means in Nonparametric Regression