Goodness-of-fit tests for parametric regression models based on empirical characteristic functions

Marie Hušková; Simon G. Meintanis

Kybernetika (2009)

• Volume: 45, Issue: 6, page 960-971
• ISSN: 0023-5954

Access Full Article

top

 Access to full text

 Full (PDF)

Abstract

top

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.

How to cite

top

• MLA
• BibTeX
• RIS

Hušková, Marie, and Meintanis, Simon G.. "Goodness-of-fit tests for parametric regression models based on empirical characteristic functions." Kybernetika 45.6 (2009): 960-971. <http://eudml.org/doc/37688>.

@article{Hušková2009,
abstract = {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.},
author = {Hušková, Marie, Meintanis, Simon G.},
journal = {Kybernetika},
keywords = {empirical characteristic function; kernel regression estimators; empirical characteristic function; kernel regression estimators},
language = {eng},
number = {6},
pages = {960-971},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Goodness-of-fit tests for parametric regression models based on empirical characteristic functions},
url = {http://eudml.org/doc/37688},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Hušková, Marie
AU - Meintanis, Simon G.
TI - Goodness-of-fit tests for parametric regression models based on empirical characteristic functions
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 6
SP - 960
EP - 971
AB - 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.
LA - eng
KW - empirical characteristic function; kernel regression estimators; empirical characteristic function; kernel regression estimators
UR - http://eudml.org/doc/37688
ER -

References

top

1. A multivariate empirical characteristic function test of independence with normal marginals, J. Multivariate Anal. 95 (2005), 345–369. MR2170401
2. Testing goodness-of-fit in logistic case-control studies, Biometrika 94 (2007), 487–495. Zbl1132.62020MR2380573
3. A consistent test for the functional form of a regression function based on a difference of variance estimators, Ann. Statist. 27 (1999), 1012–1040. MR1724039
4. Testing lack-of-fit of parametric regression models using nonparametric regression techniques, Statistica Sinica 15 (2005), 135–152. MR2125724
5. Goodness-of-fit tests for parametric regression models, J. Amer. Statist. Assoc. 96 (2001), 640–652. MR1946431
6. Testing for affine equivalence of elliptically symmetric distributions, J. Multivariate Anal. 88 (2004), 222–242. MR2025611
7. Comparing nonparametric versus parametric regression fits, Ann. Statist. 21 (1993), 1926–1947. MR1245774
8. Invariant tests for symmetry about an unspecified point based on the empirical characteristic function, J. Multivariate Anal. 87 (2003), 275–297. MR2016939
9. Change point analysis based on empirical characteristic functions, Metrika 63 (2006), 145–168. MR2242537
10. Tests for the error distribution in nonparametric possibly heteroscedastic regression models, To appear in Test. 
11. A consistent modification of a test for independence based on the empirical characteristic function, J. Math. Sci. 89 (1998), 1486–1494. MR1632247
12. A simple consistent bootstrap test for a parametric regression function, J. Econometrics 87 (1998), 145–165. MR1648892
13. Permutation tests for homogeneity based on the empirical characteristic function, J. Nonparametr. Statist. 17 (2005), 583–592. Zbl1065.62084MR2141363
14. A bootstrap version of the residual-based smooth empirical distribution function, J. Nonparametr. Statist. 20 (2008), 153–174. Zbl1141.62027MR2407963
15. Bootstrap approximation in model checks for regression, J. Amer. Statist. Assoc. 93 (1998), 141–149. MR1614600
16. Goodness-of-fit tests in parametric regression based on the estimation of the error distribution, Test 17 (2008), 401–415. MR2434335
17. Nonlinear Regression, Wiley, New York 1989, pp. 501–513. MR0986070
18. Consistent bootstrap tests of parametric regression functions, J. Econometrics 98 (2000), 27–46. MR1790649
19. Consequences and detection of misspecified nonlinear regression models, J. Amer. Statist. Assoc. 76 (1981), 419–433. Zbl0467.62058MR0624344
20. Maximum likelihood estimation of misspecified models, Econometrica 50 (1982), 1–25. Zbl0518.62092MR0640163
21. Asymptotic theory of nonlinear least-squares estimation, Ann. Statist. 9 (1981) 501–513. Zbl0475.62050MR0615427
22. Handbook of Function and Generalized Function Transformations, CRC Press, New York 1996. Zbl0851.44002MR1392476

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget. български (bg) čeština (cs) Deutsch (de) ελληνικά (el) English (en) español (es) français (fr) italiano (it) lietuvių kalba (lt) polski (pl) português (pt) română (ro) русский (ru) slovenčina (sk)

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page 5 10 15 20

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.

OK