Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-25T16:04:16.194Z Has data issue: false hasContentIssue false
  • English
  • Français

SPECIFICATION TESTING WHEN THE NULL IS NONPARAMETRIC OR SEMIPARAMETRIC

Published online by Cambridge University Press:  18 September 2014

Juan M. Rodríguez-Póo ,
Stefan Sperlich  and
Philippe Vieu
Juan M. Rodríguez-Póo*
Affiliation:
Universidad de Cantabria
Stefan Sperlich
Affiliation:
Université de Genève
Philippe Vieu
Affiliation:
Université Paul Sabatier
*
*Address correspondence to Juan Manuel Rodriguez-Poo, Departamento de Economía, Universidad de Cantabria, Avda. de los Castros s/n, 39005, Santander, Spain; e-mail: rodrigjm@unican.es
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses the problem of testing misspecifications in semiparametric regression models for a large family of econometric models under rather general conditions. We focus on two main issues that typically arise in econometrics. First, many econometric models are estimated through maximum likelihood or pseudo-ML methods like, for example, limited dependent variable or gravity models. Second, often one might not want to fully specify the null hypothesis. Instead, one would rather impose some structure like separability or monotonicity. In order to address these points we introduce an adaptive omnibus test. Special emphasis is given to practical issues like adaptive bandwidth choice, general but simple requirements on the estimates, and finite sample performance, including the resampling approximations.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 6 , December 2015 , pp. 1281 - 1309
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Amemiya, T. (1973) Regression analysis when the dependent variable is truncated normal. Econometrica 41, 997–1016.CrossRefGoogle Scholar
Delgado, M.A., Rodriguez-Poó, J.M., & Wolf, M. (2001) Subsampling cube root asymptotics with an application to Manski’s MSE. Economics Letters 73, 241–250.CrossRefGoogle Scholar
Dette, H., von Lieres und Wilkau, C., & Sperlich, S. (2005) A comparison of different nonparametric methods for inference on additive models. Journal of Nonparametric Statistics 17, 57–81.CrossRefGoogle Scholar
Giné, E. & Zinn, J. (1990) Bootstrapping general empirical measures. Annals of Probability 18, 851–869.CrossRefGoogle Scholar
Gonzalez-Manteiga, W. & Crujeiras, R.M. (2013) An updated review of goodness-of-fit tests for regression models. With discussion. Test 22, 361–447.CrossRefGoogle Scholar
Guerre, E. & Lavergne, P. (2002) Optimal minimax rates for nonparametric specification testing in regression models. Econometric Theory 18, 1139–1171.CrossRefGoogle Scholar
Guerre, E. & Lavergne, P. (2005) Rate-optimal data-driven specification testing for regression models. Annals of Statistics 33, 840–870.CrossRefGoogle Scholar
Härdle, W., Huet, S., Mammen, E., & Sperlich, S. (2004) Bootstrap inference in semiparametric generalized additive models. Econometric Theory 20, 265–300.CrossRefGoogle Scholar
Härdle, W., Sperlich, S., & Spokoiny, V. (2001) Structural tests in additive regression. Journal of the American Statistical Association 96, 1333–1347.CrossRefGoogle Scholar
Hart, J. (1997) Nonparametric Smoothing and Lack-of-Fit Tests. Springer Series in Statistics. Springer.Google Scholar
Horowitz, J. & Spokoiny, V. (2001) An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative. Econometrica 69, 599–632.CrossRefGoogle Scholar
Kallenberg, W.C.M. & Ledwina, T. (1995) Consistency and Monte Carlo simulation of a data driven version of smooth goodness-of-fit tests. Annals of Statistics 23, 1594–1608.CrossRefGoogle Scholar
Köhler, M., Schindler, A., & Sperlich, S. (2014) A review and comparison of bandwidth selection methods for kernel regression. International Statistical Review 61, 405–415.Google Scholar
Lewbel, A. & Linton, O. (2002) Nonparametric censored and truncated regression. Econometrica 70, 765–779.CrossRefGoogle Scholar
Lewbel, A. & Linton, O. (2007) Nonparametric matching and homothetically separable functions. Econometrica 75, 1209–1228.CrossRefGoogle Scholar
Mack, Y.P. & Silverman, B.W. (1982) Weak and strong uniform consistency of kernel regression estimates. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 61, 405–415.CrossRefGoogle Scholar
Neumeyer, N. & Sperlich, S. (2006) Comparison of separable components in different samples. Scandinavian Journal of Statistics 33, 477–501.CrossRefGoogle Scholar
Pardo-Fernández, J.C., Van Keilegom, I., & González-Manteiga, W. (2007) Goodness-of-fit tests for parametric models in censored regression. Canadian Journal of Statistics 35, 249–264.CrossRefGoogle Scholar
Politis, D.N., Romano, J.P., & Wolf, M. (1999) Subsampling. Springer-Verlag.CrossRefGoogle Scholar
Politis, D.N., Romano, J.P., & Wolf, M. (2001) On the asymptotic theory of subsampling. Statistica Sinica 11, 1105–1124.Google Scholar
Roca-Pardiñas, J. & Sperlich, S. (2007) Testing the link when the index is semiparametric – A comparative study. Computational Statistics & Data Analysis 12, 6565–6581.CrossRefGoogle Scholar
Rodríguez-Póo, J., Sperlich, S., & Vieu, P. (2003) Semiparametric estimation of separable models with possibly limited dependent variables. Econometric Theory 19, 1008–1040.CrossRefGoogle Scholar
Rodríguez-Póo, J., Sperlich, S., & Vieu, P. (2012) A Practical Test for Misspecification in Regression: Functional Form, Separability and Distribution. Working paper WPS 12-09-3, University of Geneva.Google Scholar
Severini, T.A. & Wong, W.W. (1992) Profile likelihood and conditionally parametric models. Annals of Statistics 4, 1768–1802.Google Scholar
Sperlich, S. (2013) On the choice of regularization parameters in specification testing: A critical discussion. Empirical Economics, in press.Google Scholar
Sperlich, S., Tjøstheim, D., & Yang, L. (2002) Nonparametric estimation and testing of interaction in additive models. Econometric Theory 18, 197–251.CrossRefGoogle Scholar
Spokoiny, V. (2001) Data-driven testing the fit of linear models. Mathematical Methods of Statistics 10, 465–497.Google Scholar
Stone, C.J. (1982) Optimal global rates of convergence for nonparametric regression. Annals of Statistics 10, 1040–1053.CrossRefGoogle Scholar
Zheng, J.X. (1996) A consistent test of functional form via nonparametric estimation techniques. Journal of Econometrics 75, 263–289.CrossRefGoogle Scholar