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TEST

, Volume 17, Issue 2, pp 401–415 | Cite as

Goodness-of-fit tests in parametric regression based on the estimation of the error distribution

  • Ingrid Van Keilegom
  • Wenceslao González ManteigaEmail author
  • César Sánchez Sellero
Original Paper

Abstract

Consider a heteroscedastic regression model Y=m(X)+σ(X)ε, where m(X)=E(Y|X) and σ 2(X)=Var (Y|X) are unknown, and the error ε is independent of the covariate X. We propose a new type of test statistic for testing whether the regression curve m(⋅) belongs to some parametric family of regression functions. The proposed test statistic measures the distance between the empirical distribution function of the parametric and of the nonparametric residuals. The asymptotic theory of the proposed test is developed, and the proposed testing procedure is illustrated by means of a small simulation study and the analysis of a data set.

Keywords

Bootstrap Goodness-of-fit Heteroscedastic regression Model check Nonlinear regression Nonparametric regression Residual distribution 

Mathematics Subject Classification (2000)

62G10 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2007

Authors and Affiliations

  • Ingrid Van Keilegom
    • 1
  • Wenceslao González Manteiga
    • 2
    Email author
  • César Sánchez Sellero
    • 2
  1. 1.Institut de StatistiqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Departamento de Estadística, Facultad de MatemáticasUniversidad de Santiago de CompostelaSantiago de CompostelaSpain

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