zbMATH — the first resource for mathematics

Tests for the error distribution in nonparametric possibly heteroscedastic regression models. (English) Zbl 1203.62069
Summary: Consistent procedures are constructed for testing the goodness-of-fit of the error distribution in nonparametric regression models. The test starts with a kernel-type regression fit and proceeds with the construction of a test statistic in the form of an \(L _{2}\) distance between a parametric and a nonparametric estimates of the residual characteristic function. The asymptotic null distribution and the behavior of the test statistic under alternatives are investigated. A simulation study compares bootstrap versions of the proposed test to corresponding procedures utilizing the empirical distribution function.

62G08 Nonparametric regression and quantile regression
62E20 Asymptotic distribution theory in statistics
62G30 Order statistics; empirical distribution functions
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI
[1] Akritas MG, Van Keilegom I (2001) Non-parametric estimation of the residual distribution. Scand J Statist 28:549–567 · Zbl 0980.62027 · doi:10.1111/1467-9469.00254
[2] Chen X, White H (1998) Central limit and functional central limit theorems for Hilbert-valued dependent heterogeneous arrays with applications. Econom Theory 14:260–284
[3] Dehling H (1983) Limit theorems for sums of weakly dependent Banach space valued random variables. Z Wahrscheinlichtkeitstheor Verw Geb 63:393–432 · Zbl 0496.60004 · doi:10.1007/BF00542537
[4] Epps TW (2005) Tests for location-scale families based on the empirical characteristic function. Metrika 62:99–114 · Zbl 1080.62010 · doi:10.1007/s001840400358
[5] Hušková M, Meintanis SG (2007) Omnibus test for the error distribution in the linear regression model. Statistics 41:363–376 · Zbl 1126.62059 · doi:10.1080/02331880701442643
[6] Jiménez Gamero MD, Muñoz Garcia J, Pino Mejias R (2005) Testing goodness of fit for the distribution of errors in multivariate linear models. J Multivar Anal 95:301–322 · Zbl 1070.62029 · doi:10.1016/j.jmva.2004.08.010
[7] Jurečková J, Picek J, Sen PK (2003) Goodness-of-fit tests with nuisance regression and scale. Metrika 58:235–258 · Zbl 1042.62036 · doi:10.1007/s001840300262
[8] Khmaladze EV, Koul HL (2004) Martingale transforms goodness-of-fit tests in regression models. Ann Statist 32:995–1034 · Zbl 1092.62052 · doi:10.1214/009053604000000274
[9] Neumeyer N (2006) Bootstrap procedures for empirical processes of nonparametric residuals. Habilitationsschrift, Ruhr-Universität, Bochum
[10] Neumeyer N, Dette H, Nagel E-R (2006) Bootstrap test for the error distribution in linear and nonparametric regression models. Aust N Z J Stat 48:129–156 · Zbl 1108.62032 · doi:10.1111/j.1467-842X.2006.00431.x
[11] Sen PK, Jurečková J, Picek J (2003) Goodness-of-fit test of Shapiro–Wilk type with nuisance regression and scale. Aust J Stat 32:163–177
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.