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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.

MSC:
62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62G20 Asymptotic properties of nonparametric inference
Software:
fda (R)
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References:
[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
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