Resampling for checking linear regression models via non-parametric regression estimation

✍ Scribed by J.M.Vilar Fernández; W.González Manteiga

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 359 KB
• Volume: 35
• Category: Article
• ISSN: 0167-9473
• DOI: 10.1016/s0167-9473(99)00117-6

✦ Synopsis

Let us consider the ÿxed regression model, Yt = m(xt) + t ; t = 1; : : : ; n; and assume that the random errors, { t }; follow an ARMA-type dependence structure. The purpose of this paper is to study the application of the bootstrap test to check that the unknown regression function, m, follows a general linear model of the type:

with A being a functional of R in R q . In a previous paper, Gonzà alez-Manteiga and Vilar-Fernà andez (1995) proposed a test, D = d 2 ( mn; m Ân ), based on the Crà amer-von-Mises-type functional distance, where mn is a Gasser-M uller-type non-parametric estimator of m; and m Ân is a member of the family M that is closest to mn. In this work, two bootstrap algorithms are considered, where the dependence structure of the errors is taken into account. A broad simulation study and an applied example show the good behavior of the bootstrap test.