Hostname: page-component-89b8bd64d-72crv Total loading time: 0 Render date: 2026-05-07T14:39:39.142Z Has data issue: false hasContentIssue false
  • English
  • Français

SPECIFICATION TEST FOR CONDITIONAL DISTRIBUTION WITH FUNCTIONAL DATA

Published online by Cambridge University Press:  02 August 2011

Frederic Ferraty ,
Alejandro Quintela-del-Río  and
Philippe Vieu
Frederic Ferraty
Affiliation:
Université Paul Sabatier
Alejandro Quintela-del-Río*
Affiliation:
Universidad de A Coruña
Philippe Vieu
Affiliation:
Université Paul Sabatier
*
*Address correspondence to Alejandro Quintela-del-Río, Universidad de A Coruña, Campus de Elviña s/n, 15071 A. Coruña, Spain; e-mail: aquintela@udc.es.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we construct a statistic to test a specific form of the conditional density function. The main point of this work is to consider a functional explanatory variable, and the statistic is constructed following recent advances in nonparametric functional data analysis. The asymptotic behavior of the test statistic is studied under both the null hypothesis and some local alternative hypothesis. Then, the finite sample behavior of the method is studied through simulated examples. This paper is one of the first in the setting of nonparametric specification tests when functional data are involved.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 28 , Issue 2 , April 2012 , pp. 363 - 386
Copyright
Copyright © Cambridge University Press 2011

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Alva, K., Romo, J., & Ruiz, E. (2009) Modeling Intra-daily Volatility by Functional Data Analysis: An Empirical Application to the Spanish Stock Market. Working Paper 09-28, Statistics and Econometrics Series, University Carlos III.Google Scholar
Bogachev, V.I. (1999) Gaussian Measures. Mathematical surveys and monographs 62. American Mathematical Society.Google Scholar
Bugni, F.A., Hall, P., Horowitz, J.L., & Neumann, G.R. (2009) Goodness-of-fit tests for functional data. Econometrics Journal 12, 1–18.CrossRefGoogle Scholar
Cai, Z. & Wang, X. (2008) Nonparametric estimation of conditional VaR and expected shortfall. Journal of Econometrics 147, 120–130.CrossRefGoogle Scholar
Chen, X., Linton, O., & Robinson, P. (2000) The estimation of conditional densities. In Puri, M.L. (ed.), Asymptotics in Statistics and Probability: Papers in Honor of George Roussas, pp. 71–84. VSP International Science Publishers.CrossRefGoogle Scholar
De Jong, P. (1987) A central limit theorem for generalized quadratic forms. Probability Theory and Related Fields 75, 261–277.CrossRefGoogle Scholar
Delgado, M. & González-Manteiga, W. (2001) Significance testing in nonparametric regression based on the bootstrap. Annals of Statistics 29, 1469–1507.Google Scholar
Delsol, L. (2008) Regression sur variables fonctionnelles: Estimation, tests de structure et estimation. Ph.D. thesis, Universite Paul Sabatier.Google Scholar
Fan, J. (2005) A selective overview of nonparametric methods in financial econometrics. Statistical Science 20, 317–337.Google Scholar
Fan, Y. & Li, Q. (1996) Consistent model specification tests: Omitted variables and semi-parametric functional forms. Econometrica 64, 865–890.CrossRefGoogle Scholar
Fernandes, M. & Grammig, J. (2005) Nonparametric specification tests for conditional duration models. Journal of Econometrics 127, 35–68.Google Scholar
Ferraty, F., Laksaci, A., & Vieu, P. (2006) Estimating some characteristics of the conditional distribution in nonparametric functional models. Statistical Inference for Stochastic Processes 9, 47–76.CrossRefGoogle Scholar
Ferraty, F., Van Keilegom, I., & Vieu, P. (2010) On the validity of the bootstrap in nonparametric functional regression. Scandinavian Journal of Statistics 37, 286–306.CrossRefGoogle Scholar
Ferraty, F. & Vieu, P. (2006) Nonparametric Functional Data Analysis. Springer Series in Statistics. Springer.Google Scholar
Guerre, E. & Lavergne, P. (2002) Optimal minimax rates for nonparametric specification testing in regression models. Econometric Theory 18, 1139–1171.Google Scholar
Hansen, B. (1994) Autoregressive conditional density estimation. International Economic Review 35, 705–730.CrossRefGoogle Scholar
Härdle, W. & Mammen, E. (1993) Comparing parametric versus nonparametric regression fits. Annals of Statistics 21, 1926–1947.CrossRefGoogle Scholar
Hart, J. (1997) Nonparametric Smoothing and Lack of Fit Tests. Springer.CrossRefGoogle Scholar
Hyndman, R.J. & Yao, Q. (2002) Nonparametric estimation and symmetry tests for conditional density functions. Journal of Nonparametric Statistics 14, 259–278.Google Scholar
Jank, W. & Shmuel, G. (2006) Functional data analysis in electronic commerce research. Statistical Science 21, 155–166.CrossRefGoogle Scholar
Laukaitis, A. (2008) Functional data analysis for cash flow and transactions intensity continuous-time prediction using Hilbert-valued autoregressive processes. European Journal of Operational Research 185, 1607–1614.Google Scholar
Li, W.V. & Shao, Q.M. (2001) Gaussian processes: Inequalities, small ball probabilities and applications. In Rao, C.R. and Shanbhag, D. (eds.), Stochastic Processes: Theory and Methods. Handbook of Statistics 19. North-Holland.Google Scholar
Linton, O. & Sancetta, A. (2009) Consistent estimation of a general nonparametric regression function in time series. Journal of Econometrics 152, 70–78.CrossRefGoogle Scholar
Racine, J.S. (2008) Nonparametric econometrics: A primer. Foundations and Trends in Econometrics 3, 1–88.Google Scholar
Ramsay, J.O., Hooker, G., & Graves, S. (2009) Functional Data Analysis with R and MATLAB. Springer.CrossRefGoogle Scholar
Ramsay, J.O. & Ramsey, J.B. (2002) Functional data analysis of the dynamics of the monthly index of nondurable goods production. Journal of Econometrics 107, 327–344.Google Scholar
Ramsay, J.O. & Silverman, B. (2002) Applied Functional Data Analysis, Methods and Case Studies. Springer Series in Statistics. Springer.Google Scholar
Ramsay, J.O. & Silverman, B. (2005) Functional Data Analysis (2nd ed.). Springer Series in Statistics. Springer.CrossRefGoogle Scholar
Reddy, S.K. & Dass, M. (2006) Modeling on-line art auction dynamics using functional data analysis. Statistical Science 21, 179–193.Google Scholar