, Volume 22, Issue 3, pp 361–411

An updated review of Goodness-of-Fit tests for regression models

  • Wenceslao González-Manteiga
  • Rosa M. Crujeiras
Invited Paper

DOI: 10.1007/s11749-013-0327-5

Cite this article as:
González-Manteiga, W. & Crujeiras, R.M. TEST (2013) 22: 361. doi:10.1007/s11749-013-0327-5


This survey intends to collect the developments on Goodness-of-Fit for regression models during the last 20 years, from the very first origins with the proposals based on the idea of the tests for density and distribution, until the most recent advances for complex data and models. Far from being exhaustive, the contents in this paper are focused on two main classes of tests statistics: smoothing-based tests (kernel-based) and tests based on empirical regression processes, although other tests based on Maximum Likelihood ideas will be also considered. Starting from the simplest case of testing a parametric family for the regression curves, the contributions in this field provide also testing procedures in semiparametric, nonparametric, and functional models, dealing also with more complex settings, as those ones involving dependent or incomplete data.


Bootstrap calibration Empirical distribution of the residuals Empirical regression process Likelihood ratio tests Smoothing tests 

Mathematics Subject Classification

62G08 62G09 62G10 

Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  • Wenceslao González-Manteiga
    • 1
  • Rosa M. Crujeiras
    • 1
  1. 1.Dpt. of Statistics and Operations Research, Faculty of MathematicsUniversity of Santiago de CompostelaSantiago de CompostelaSpain

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