Abstract
In many applications, covariates are not observed but have to be estimated from data. We outline some regression-type models where such a situation occurs and discuss estimation of the regression function in this context. We review theoretical results on how asymptotic properties of nonparametric estimators differ in the presence of generated covariates from the standard case where all covariates are observed. These results also extend to settings where the focus of interest is on average functionals of the regression function.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Heckman, J.J., Vytlacil, E.J.: Structural equations, treatment effects, and econometric policy evaluation. Econometrica 73, 669–738 (2005)
Heckman, J.J., Vytlacil, E.J.: Econometric evaluation of social programs, Part II: using the marginal treatment effect to organize alternative econometric estimators to evaluate social programs, and to forecast their effects in new environments. In: Heckman, J.J., Leamer, E.E. (eds.) Handbook of Econometrics, vol. 6, chapter 71. Elsevier, Amsterdam (2007)
Imbens, G.W., Newey, W.K.: Identification and estimation of triangular simultaneous equations models without additivity. Econometrica 77, 1481–1512 (2009)
Linton, O., Nielsen, J.P.: Kernel estimation of partial means and a general variance estimator. Biometrika 82, 93–100 (1995)
Mammen, E., Linton, O., Nielsen, J.P.: The existence and asymptotic properties of a backfitting algorithm under weak conditions. Ann. Stat. 27, 1443–1490 (1999)
Mammen, E., Rothe, C., Schienle, M.: Nonparametric regression with nonparametrically generated covariates. Ann. Stat. 40, 1132–1170 (2012)
Mammen, E., Rothe, C., Schienle, M.: Semiparametric estimation with generated covariates. Preprint (2012)
Newey, W.K.: A kernel method of estimating structured nonparametric regression based on marginal integration. Econometric Theory 10, 233–253 (1994)
Newey, W.K., Powell, J.L., Vella, F.: Nonparametric estimation of triangular simultaneous equations models. Econometrica 67, 565–603 (1999)
Tjøstheim, D., Auestad, B.H.: Nonparametric identification of nonlinear time series: selecting significant lags. J. Am. Stat. Assoc. 89 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mammen, E., Rothe, C., Schienle, M. (2013). Generated Covariates in Nonparametric Estimation: A Short Review. In: Oliveira, P., da Graça Temido, M., Henriques, C., Vichi, M. (eds) Recent Developments in Modeling and Applications in Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32419-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-32419-2_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32418-5
Online ISBN: 978-3-642-32419-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)