zbMATH — the first resource for mathematics

Semi-functional partial linear regression. (English) Zbl 1090.62036
Summary: This paper deals with the problem of predicting some real-valued response variables in the situation where some among the explanatory variables are functional. More precisely, a new model is introduced in order to capture both the advantages of a semi-linear modelling and those of the recent advances on nonparametric statistics for functional data. The aim is to provide first advances in this direction. After having constructed precisely the so-called semi-functional partially linear model, the estimates are presented and some asymptotic results (with rates of convergence) are given. Lastly, a real data example illustrates the usefulness of the model.

62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
fda (R)
PDF BibTeX Cite
Full Text: DOI
[1] Aneiros-Pérez, G.; González-Manteiga, W.; Vieu, P., Estimation and testing in a partial linear regression model under long-memory dependence, Bernoulli, 10, 49-78, (2004) · Zbl 1040.62028
[2] Bhattacharya, P.K.; Zhao, P.-L., Semiparametric inference in a partial linear model, Ann. statist., 25, 244-262, (1997) · Zbl 0869.62050
[3] Cardot, H.; Ferraty, F.; Sarda, P., Spline estimators for the functional linear model, Statist. sinica, 13, 571-591, (2003) · Zbl 1050.62041
[4] Chen, H., Convergence rates for parametric components in a partly linear model, Ann. statist., 16, 136-146, (1988) · Zbl 0637.62067
[5] Engle, R.; Granger, C.; Rice, J.; Weiss, A., Nonparametric estimates of the relation between weather and electricity sales, J. amer. statist. assoc., 81, 310-320, (1986)
[6] Ferraty, F.; Vieu, P., Nonparametric models for functional data, with application in regression, time-series prediction and curve discrimination, J. nonparametric statist., 16, 111-125, (2004) · Zbl 1049.62039
[7] Ferraty, F.; Vieu, P., Nonparametric functional data analysis, (2006), Springer New York, in press · Zbl 1049.62039
[8] Gao, J.T., The laws of the iterated logarithm of some estimates in partly linear models, Statist. probab. lett., 25, 153-162, (1995) · Zbl 0837.62041
[9] Härdle, W.; Liang, H.; Gao, J., Partially linear models, (2000), Physica-Verlag
[10] Hastie, T.J.; Tibshirani, R.J., Generalized additive models, (1990), Chapman & Hall New York · Zbl 0747.62061
[11] Liang, H., An application of Bernstein’s inequality, Econom. theory, 15, 152, (1999)
[12] Liang, H., Asymptotic normality of parametric part in partially linear models with measurement error in the nonparametric part, J. statist. plann. inference, 86, 51-62, (2000) · Zbl 0952.62036
[13] Ramsay, J.; Silverman, B., Applied functional data analysis. methods and case studies, (2002), Springer Berlin · Zbl 1011.62002
[14] Ramsay, J.; Silverman, B., Functional data analysis, (2005), Springer Berlin · Zbl 1079.62006
[15] Ritov, Y.; Bickel, P.J., Achieving information bounds in non and semiparametric models, Ann. statist., 18, 925-938, (1990) · Zbl 0722.62025
[16] Schick, A., Root-n consistent estimation in partly linear regression models, Statist. probab. lett., 28, 353-358, (1996) · Zbl 0897.62040
[17] Speckman, P., Kernel smoothing in partial linear models, J. roy. statist. soc. ser. B, 50, 413-436, (1988) · Zbl 0671.62045
[18] Stout, W., Almost sure convergence, (1974), Academic Press New York · Zbl 0321.60022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.