Previous |  Up |  Next


empirical characteristic function; kernel regression estimators
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.
[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
[2] H. D. Bondell: Testing goodness-of-fit in logistic case-control studies. Biometrika 94 (2007), 487–495. MR 2380573 | Zbl 1132.62020
[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
[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
[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
[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
[7] W. Härdle and E. Mammen: Comparing nonparametric versus parametric regression fits. Ann. Statist. 21 (1993), 1926–1947. MR 1245774
[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
[9] M. Hušková and S. G. Meintanis: Change point analysis based on empirical characteristic functions. Metrika 63 (2006), 145–168. MR 2242537
[10] M. Hušková and S. G. Meintanis: Tests for the error distribution in nonparametric possibly heteroscedastic regression models. To appear in Test.
[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
[12] Qi Li and Suojin Wang: A simple consistent bootstrap test for a parametric regression function. J. Econometrics 87 (1998), 145–165. MR 1648892
[13] S. G. Meintanis: Permutation tests for homogeneity based on the empirical characteristic function. J. Nonparametr. Statist. 17 (2005), 583–592. MR 2141363 | Zbl 1065.62084
[14] N. Neumeyer: A bootstrap version of the residual-based smooth empirical distribution function. J. Nonparametr. Statist. 20 (2008), 153–174. MR 2407963 | Zbl 1141.62027
[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
[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
[17] G. A. F. Seber and C. J. Wild: Nonlinear Regression. Wiley, New York 1989, pp. 501–513. MR 0986070
[18] Yoon-Jae Whang: Consistent bootstrap tests of parametric regression functions. J. Econometrics 98 (2000), 27–46. MR 1790649
[19] H. White: Consequences and detection of misspecified nonlinear regression models. J. Amer. Statist. Assoc. 76 (1981), 419–433. MR 0624344 | Zbl 0467.62058
[20] H. White: Maximum likelihood estimation of misspecified models. Econometrica 50 (1982), 1–25. MR 0640163 | Zbl 0518.62092
[21] C. F. Wu: Asymptotic theory of nonlinear least-squares estimation. Ann. Statist. 9 (1981) 501–513. MR 0615427 | Zbl 0475.62050
[22] A. I. Zayed: Handbook of Function and Generalized Function Transformations. CRC Press, New York 1996. MR 1392476 | Zbl 0851.44002
Partner of
EuDML logo