Goodness-of-fit tests for censored regression based on artificial data points

• Wenceslao González Manteiga ^[1] ; César Sánchez Sellero ^[1] ; Cédric Heuchenne ^[2] ; Alessandro Beretta ^[2]
  1. [1] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
  2. [2] University of Liège

     University of Liège

     Arrondissement de Liège, Bélgica

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 29, Nº. 2, 2020, págs. 599-615
• Idioma: inglés
• DOI: 10.1007/s11749-019-00662-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • Suppose we have a location-scale regression model where the location is the conditional mean and the scale is the conditional standard deviation; the response is possibly right-censored, the covariate is fully observed, and the error is independent of the covariate. We propose new goodness-of-fit testing procedures for the conditional mean and variance based on an integrated regression function technique which uses artificial data points. We obtain the weak convergence of the resulting processes and study their finite sample behavior via simulations. Finally, we analyze a data set about unemployment in Galicia.

• Referencias bibliográficas
  • Beran R (1981) Nonparametric regression with randomly censored survival data. Technical Report, Univ, California, Berkeley
  • Billingsley P (1968) Convergence of probability measures. Wiley, New York
  • Dette H, Heuchenne C (2012) Scale checks in censored regression. Scand J Stat 39:323–339
  • Efron B (1981) Censored data and the bootstrap. J Am Stat Assoc 76:312–319
  • Heuchenne C, Laurent G (2017) Parametric conditional variance estimation in location-scale models with censored data. Electronic J Stat 11:148–176
  • Heuchenne C, Van Keilegom I (2007) Polynomial regression with censored data based on preliminary nonparametric estimation. Ann Inst Stat Math...
  • Heuchenne C, Van Keilegom I (2008a) Nonlinear regression with censored data. Technometrics 49:34–44
  • Heuchenne C, Van Keilegom I (2008b) Location estimation in nonparametric regression with censored data. J Multivar Anal 98:1558–1582
  • Heuchenne C, Van Keilegom I (2010) Estimation in nonparametric location-scale regression models with censored data. Ann Inst Stat Math 62:439–463
  • Heuchenne C, Van Keilegom I (2012) Estimation of a general parametric location in censored regression. In: Van Keilegom I, Wilson PW (eds)...
  • Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481
  • Levenberg K (1944) A method for the solution of certain problems in least squares. Q Appl Math 2:164–168
  • Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441
  • Pardo-Fernández JC, Van Keilegom I, González-Manteiga W (2007) Goodness-of-fit tests for parametric models in censored regression. Can J Stat...
  • Rao CR (1965) Linear statistical inference and its applications. Wiley, New York
  • Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New York
  • Stute W (1993) Consistent estimation under random censorship when covariables are present. J Multivar Anal 45:89–103
  • Stute W (1997) Nonparametric model checks for censored regression. Ann Stat 25:613–641
  • Stute W (1999) Nonlinear censored regression. Stat Sinica 9:1089–1102
  • Stute W, González Manteiga W, Sánchez Sellero C (2000) Nonparametric model checks in censored regression. Commun Stat Theory Methods 29:1611–1629
  • Van Keilegom I, Akritas MG (1999) Transfer of tail information in censored regression models. Ann Stat 27:1745–1784