No CrossRef data available.
Article contents
SPECIFICATION AND ESTIMATION OF SEMIPARAMETRIC MULTIPLE-INDEX MODELS
Published online by Cambridge University Press: 17 July 2008
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
We propose an easy to use derivative-based two-step estimation procedure for semiparametric index models, where the number of indexes is not known a priori. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators, in particular the average outer product of the gradient (AOPG). By testing the rank of the AOPG we determine the required number of indexes. Subsequently, we estimate the index parameters in a method of moments framework, with moment conditions constructed using the estimated average derivative functionals. The estimator readily extends to multiple equation models and is shown to be root-N-consistent and asymptotically normal.
Information
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 2008
References
REFERENCES
Andrews, D.W.K. (1987) Asymptotic results for generalized Wald tests. Econometric Theory 3, 348–358.CrossRefGoogle Scholar
Cragg, J.G. & Donald, S.G. (1997) Inferring the rank of a matrix. Journal of Econometrics 76, 223–250.CrossRefGoogle Scholar
Delecroix, M., Härdle, W., & Hristache, M. (2003) Efficient estimation in conditional single-index regression. Journal of Multivariate Analysis 86, 213–226.CrossRefGoogle Scholar
Donald, S.G., Fortuna, N., & Pipiras, V. (2007) On rank estimation in symmetric matrices: The case of indefinite matrix estimators. Econometric Theory 23, 1217–1232.Google Scholar
Donkers, B. & Schafgans, M. (2005) A Method of Moments Estimator for Semiparametric Index Models. Sticerd Working paper EM/2005/493, London School of Economics.Google Scholar
Dufour, J.-M. (2006) Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics. Journal of Econometrics 133, 443–477.CrossRefGoogle Scholar
Fan, J., Härdle, W., & Mammen, E. (1998) Direct estimation of low-dimensional components in additive models. Annals of Statistics 26, 943–971.Google Scholar
Friedman, J.H. & Stuetzle, W. (1981) Projection pursuit regression. Journal of the American Statistical Association 76, 817–823.CrossRefGoogle Scholar
Gill, L. & Lewbel, A. (1992) Testing the rank and definiteness of estimated matrices with applications to factor, state-space and ARMA models. Journal of the American Statistical Association 87, 766–776.Google Scholar
Härdle, W. & Stoker, T.M. (1989) Investigating smooth multiple regression by the method of average derivatives. Journal of the American Statistical Association 84, 986–995.Google Scholar
Hoeffding, W. (1948) A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics 19, 293–325.Google Scholar
Horowitz, J.L. & Härdle, W. (1996) Direct semiparametric estimation of single-index models with discrete covariates. Journal of the American Statistical Association 91, 1632–1640.Google Scholar
Hristache, M., Juditsky, A., Polzehl, J., & Spokoiny, V. (2001) Structure adaptive approach for dimension reduction. Annals of Statistics 29, 1537–1566.CrossRefGoogle Scholar
Ichimura, H. & Lee, L.F. (1991) Semiparametric least squares estimation of multiple index models: Single equation estimation. In Barnett, W.A., Powell, J., & Tauchen, G.E. (eds.), Nonparametric and Semiparametric Estimation Methods in Econometrics and Statistics, pp. 3–49. Cambridge University Press.Google Scholar
Kleibergen, F. & Paap, R. (2006) Generalized reduced rank tests using the singular value decomposition. Journal of Econometrics 133, 97–126.CrossRefGoogle Scholar
Lee, L.-F. (1995) Semiparametric maximum likelihood estimation of polychotomous and sequential choice models. Journal of Econometrics 65, 381–428.Google Scholar
Lütkepohl, H. & Burda, M.M. (1997) Modified Wald tests under nonregular conditions. Journal of Econometrics 78, 315–332.CrossRefGoogle Scholar
Magnus, J.R. & Neudecker, H. (1988) Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley.Google Scholar
Newey, W.K. (2004) Efficient semiparametric estimation via moment restrictions. Econometrica 72, 1877–1998.Google Scholar
Newey, W.K. & McFadden, D.L. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. North-Holland.Google Scholar
Phillips, P.C.B. (1994) Some exact distribution theory for maximum likelihood estimators of cointegrating coefficients in error correction models. Econometrica 62, 73–93.Google Scholar
Picone, G.A. & Butler, J.S. (2000) Semiparametric estimation of multiple equation models. Econometric Theory 16, 551–575.Google Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of weighted average derivatives. Econometrica 57, 1403–1430.CrossRefGoogle Scholar
Powell, J.L. & Stoker, T.M. (1996) Optimal bandwidth choice for density-weighted averages. Journal of Econometrics 75, 291–316.Google Scholar
Robinson, P.M. (1989) Hypothesis testing in semiparametric and nonparametric models for econometric time series. Review of Economic Studies 56, 511–534.CrossRefGoogle Scholar
Samarov, A.M. (1993) Exploring regression structure using nonparametric functional estimation. Journal of the American Statistical Association 88, 836–847.CrossRefGoogle Scholar
Stoker, T. M. (1991) Equivalence of direct, indirect, and slope estimators of average derivatives. In Barnett, W.A., Powell, J., & Tauchen, G.E. (eds.), Nonparametric and Semiparametric Estimation Methods in Econometrics and Statistics, pp. 99–118. Cambridge University Press.Google Scholar
Xia, Y., Tong, H., Li, W.K., & Zhu, L.-X. (2002) An adaptive estimation of dimension reduction space. Journal of the Royal Statistical Society, Series B 64, 363–388.Google Scholar
You have
Access
- 10
- Cited by