Previous |  Up |  Next

Article

Title: Goodness-of-fit tests for parametric regression models based on empirical characteristic functions (English)
Author: Hušková, Marie
Author: Meintanis, Simon G.
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 45
Issue: 6
Year: 2009
Pages: 960-971
Summary lang: English
.
Category: math
.
Summary: Test procedures are constructed for testing the goodness-of-fit in parametric regression models. The test statistic is in the form of an L2 distance between the empirical characteristic function of the residuals in a parametric regression fit and the corresponding empirical characteristic function of the residuals in a non-parametric regression fit. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated. Theoretical results are accompanied by a simulation study. (English)
Keyword: empirical characteristic function
Keyword: kernel regression estimators
MSC: 62F05
MSC: 62G10
MSC: 62J05
MSC: 65C60
idZBL: Zbl 1186.62029
idMR: MR2650076
.
Date available: 2010-06-02T19:27:36Z
Last updated: 2013-09-21
Stable URL: http://hdl.handle.net/10338.dmlcz/140030
.
Reference: [1] M. Bilodeau and P. de Lafaye de Micheaux: A multivariate empirical characteristic function test of independence with normal marginals.J. Multivariate Anal. 95 (2005), 345–369. MR 2170401
Reference: [2] H. D. Bondell: Testing goodness-of-fit in logistic case-control studies.Biometrika 94 (2007), 487–495. Zbl 1132.62020, MR 2380573
Reference: [3] H. Dette: A consistent test for the functional form of a regression function based on a difference of variance estimators.Ann. Statist. 27 (1999), 1012–1040. MR 1724039
Reference: [4] R. L. Eubank, Chin-Shang Li, and Suojin Wang: Testing lack-of-fit of parametric regression models using nonparametric regression techniques.Statistica Sinica 15 (2005), 135–152. MR 2125724
Reference: [5] Jianqing Fan and Li-Shan Huang: Goodness-of-fit tests for parametric regression models.J. Amer. Statist. Assoc. 96 (2001), 640–652. MR 1946431
Reference: [6] A. K. Gupta, N. Henze, and B. Klar: Testing for affine equivalence of elliptically symmetric distributions.J. Multivariate Anal. 88 (2004), 222–242. MR 2025611
Reference: [7] W. Härdle and E. Mammen: Comparing nonparametric versus parametric regression fits.Ann. Statist. 21 (1993), 1926–1947. MR 1245774
Reference: [8] N. Henze, B. Klar, and S. G. Meintanis: Invariant tests for symmetry about an unspecified point based on the empirical characteristic function.J. Multivariate Anal. 87 (2003), 275–297. MR 2016939
Reference: [9] M. Hušková and S. G. Meintanis: Change point analysis based on empirical characteristic functions.Metrika 63 (2006), 145–168. MR 2242537
Reference: [10] M. Hušková and S. G. Meintanis: Tests for the error distribution in nonparametric possibly heteroscedastic regression models.To appear in Test.
Reference: [11] A. Kankainen and N. Ushakov: A consistent modification of a test for independence based on the empirical characteristic function.J. Math. Sci. 89 (1998), 1486–1494. MR 1632247
Reference: [12] Qi Li and Suojin Wang: A simple consistent bootstrap test for a parametric regression function.J. Econometrics 87 (1998), 145–165. MR 1648892
Reference: [13] S. G. Meintanis: Permutation tests for homogeneity based on the empirical characteristic function.J. Nonparametr. Statist. 17 (2005), 583–592. Zbl 1065.62084, MR 2141363
Reference: [14] N. Neumeyer: A bootstrap version of the residual-based smooth empirical distribution function.J. Nonparametr. Statist. 20 (2008), 153–174. Zbl 1141.62027, MR 2407963
Reference: [15] W. Stute, W. Gonzáles Manteiga, and M. Presedo Quindimil: Bootstrap approximation in model checks for regression.J. Amer. Statist. Assoc. 93 (1998), 141–149. MR 1614600
Reference: [16] I. van Keilegom, W. Gonzáles Manteiga, and C. Sanchez Sellero: Goodness-of-fit tests in parametric regression based on the estimation of the error distribution.Test 17 (2008), 401–415. MR 2434335
Reference: [17] G. A. F. Seber and C. J. Wild: Nonlinear Regression.Wiley, New York 1989, pp. 501–513. MR 0986070
Reference: [18] Yoon-Jae Whang: Consistent bootstrap tests of parametric regression functions.J. Econometrics 98 (2000), 27–46. MR 1790649
Reference: [19] H. White: Consequences and detection of misspecified nonlinear regression models.J. Amer. Statist. Assoc. 76 (1981), 419–433. Zbl 0467.62058, MR 0624344
Reference: [20] H. White: Maximum likelihood estimation of misspecified models.Econometrica 50 (1982), 1–25. Zbl 0518.62092, MR 0640163
Reference: [21] C. F. Wu: Asymptotic theory of nonlinear least-squares estimation.Ann. Statist. 9 (1981) 501–513. Zbl 0475.62050, MR 0615427
Reference: [22] A. I. Zayed: Handbook of Function and Generalized Function Transformations.CRC Press, New York 1996. Zbl 0851.44002, MR 1392476
.

Files

Files Size Format View
Kybernetika_45-2009-6_6.pdf 1.010Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo