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LOCAL RANK ESTIMATION OF TRANSFORMATIONMODELS WITH FUNCTIONAL COEFFICIENTS

Published online by Cambridge University Press:  22 March 2010

Youngki Shin
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Abstract

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This paper considers a nonparametric functionalcoefficient model with an unknown link function. Themodel gives flexibility to the standardinteraction-variable model by allowing an arbitraryfunctional form of heterogeneous marginal effects.A local rank estimation procedureis proposed for the functional coefficients alongwith its asymptotic property.

Information

Type
Brief Report
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010, pp. 1807 - 1819
Copyright
Copyright © Cambridge University Press 2010

Footnotes

This paper is based on a part of my thesis. Ithank Shakeeb Khan for his encouragement andinvaluable guidance. I am also grateful to JinyongHahn (coeditor), two anonymous referees, YuliaKotlyarova, Hiro Kasahara, Sung Jae Jun, andseminar participants at various places for helpfulcomments on the previous version that led tosignificant improvements. All errors are mine.

References

REFERENCES

Abrevaya, J. (1999a) Computation of the maximum rank correlation estimator. Economics Letters 62, 279–285.CrossRefGoogle Scholar
Abrevaya, J. (1999b) Leapfrog estimation of a fixed-effects model with unknown transformation of the dependent variable. Journal of Econometrics 93, 203–228.CrossRefGoogle Scholar
Carroll, R.J., Fan, J., Gijbels, I., & Wand, M.P. (1997) Generalized partially linear single-index models. Journal of the American Statistical Association 92, 477–489.CrossRefGoogle Scholar
Cavanagh, C. & Sherman, R. (1998) Rank estimation for monotonic index models. Journal of Econometrics 84, 351–381.CrossRefGoogle Scholar
Chen, S. (2002) Rank estimation of transformation models. Econometrica 70, 1683–1697.10.1111/1468-0262.00347CrossRefGoogle Scholar
Cleveland, W.S., Grosse, E., & Shyu, W.M. (1991) Local regression models. In Chambers, J.M. & Hastie, T.J. (eds.), Statistical Models in S, pp. 309–376. Chapman and Hall.Google Scholar
Fengler, M.R., Härdle, W.K., & Mammen, E. (2007) A semiparametric factor model for implied volatility surface dynamics. Journal of Financial Econometrics 5, 189–218.CrossRefGoogle Scholar
Gelfand, A.E., Kim, H.-J., Sirmans, C.F., & Banerjee, S. (2003) Spatial modeling with spatially varying coefficient processes. Journal of the American Statistical Association 98, 387–396.10.1198/016214503000170CrossRefGoogle Scholar
Han, A. (1987) Non-parametric analysis of a generalized regression model. Journal of Econometrics 35, 303–316.CrossRefGoogle Scholar
Hastie, T. & Tibshirani, R. (1993) Varying-coefficient models. Journal of the Royal Statistical Society, Series B 55, 757–796.Google Scholar
Hoeffding, W. (1948) A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics 19, 293–325.10.1214/aoms/1177730196CrossRefGoogle Scholar
Horowitz, J. (1996) Semiparametric estimation of a regression model with an unknown transformation of the dependent variable. Econometrica 64, 103–137.10.2307/2171926CrossRefGoogle Scholar
Horowitz, J. (2001) Nonparametric estimation of a generalized additive model with an unknown link function. Econometrica 69, 499–513.CrossRefGoogle Scholar
Kauermann, G., Tutz, G., & Brüerl, J. (2005) The survival of newly founded firms: A case-study into varying-coefficient models. Journal of the Royal Statistical Society Series, A 168, 145–158.CrossRefGoogle Scholar
Khan, S. & Tamer, E. (2007) Partial rank estimation of transformation models with general forms of censoring. Journal of Econometrics 136, 251–280.CrossRefGoogle Scholar
Klein, R.W. & Sherman, R.P. (2002) Shift restrictions and semiparametric estimation in ordered response models. Econometrica 70, 663–691.CrossRefGoogle Scholar
Manski, C. (1985) Semiparametric analysis of discrete response: Asymptotic properties of maximum score estimation. Journal of Econometrics 27, 313–334.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. Elsevier.Google Scholar
Serfling, R. (1980) Approximation Theorems of Mathematical Statistics. Wiley.CrossRefGoogle Scholar
Sherman, R. (1993) The limiting distribution of the maximum rank correlation estimator. Econometrica 61, 123–137.CrossRefGoogle Scholar
Sherman, R. (1994a) Maximal inequalities for degenerate U-processes with application to optimization estimators. Annals of Statistics 22, 439–459.CrossRefGoogle Scholar
Sherman, R. (1994b) U-processes in the analysis of generalized semiparametric regression estimator. Econometric Theory 10, 372–395.CrossRefGoogle Scholar
Ye, J. & Duan, N. (1997) Nonparametric $\root \of n $-consistent estimation for the general transformation model. Annals of Statistics 25, 2682–2717.CrossRefGoogle Scholar