Partial and Recombined Estimators for Nonlinear Additive Models

Amato, U. and Antoniadis, A.: Adaptive wavelet series estimation in separable nonparametric regression models, Statistics and Computing (2001) (to appear). Ango Nze, P. and Portier, B.: Estimation of the density and the regression functions of an absolutely regular stationary process, Pub. Ins. Stat. Univ. Paris 38(2) (1994), 59–87. Auestad, B. and Tjøstheim, D.: Nonparametric identification of nonlinear time series: projections, J. Am. Stat. Assoc. 89 (1994), 1398–1409. Barry, D.: Testing for additivity of a regression function, Ann. of Stat. 21 (1993), 235–254. Bel, L., Bellanger, L., Bonneau, V., Ciuperca, G., Dacunha-Castelle, D., Deniau, C., Ghattas, B., Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J.-M. and Tomassone, R.: Eléments de comparaison de prévisions statistiques des pics d'ozone, Revue de Stat. Appl. XLVII(3) (1999a), 7–25. Bel, L., Bonneau, V., Chèze, N., Misiti, M., Misiti, Y., Oppenheim, G., Poggi, J.-M. and Portier, B.: Etudes de pollution: modèles de prévision à 3 échéances pour le dioxyde d'azote et l'ozone, Technical Report for Airparif, 215 p., July 1999b. Bel, L., Oppenheim, G., Poggi, J.-M., Portier, B. and Vautard, R.: Statistical forecasting of ozone peaks over Paris area with a nonlinear additive model. Impact of imported ozone, Proc. 10th Int. Symp. Applied Stoch. Models Data Analysis, June 12-15, 2001, Compiègne, pp. 166–171. Bosq, D.: Nonparametric Statistics for Stochastic Processes, Estimation and Prediction, Lecture Notes in Statistics, 110, Springer Verlag, New York, 1996. Breiman, L. and Friedman, J. H.: Estimating optimal transformations for multiple regression and correlation, J. Am. Stat. Assoc. 80 (1985), 580–619. Buja, A., Hastie, T. J. and Tibshirani, R. J.: Linear smoothers and additive models, Ann. of Stat. 17 (1989), 453–510. Cai, Z. and Masry, E.: Nonparametric estimation of additive nonlinear ARX time series: local linear fitting and projections, Preprint (1997), 1–30. Camlong, C.: Convergence presque sûre de l'estimateur à noyau d'une fonction de régression additive sous une hypothèse de mèlange, C. R Acad. Sci. Paris, t 329, Ser. I (1999), 75–78. Camlong-Viot, C.: Vers un test d'additivité en régression non-paramétrique sous des conditions de mélange, C. R Acad. Sci. Paris, t 333, Ser. I (2001), 877–880. Camlong-Viot, C., Sarda, P. and Vieu, P.: Additive time series: the kernel integration method, Math. Meth. Stat. 9 (2000), 358–375. Chen, R., Lui, J. S. and Tsay, R. S.: Additivity tests for nonlinear autoregression, Biometrika 82 (1995), 369–383. Collomb, G.: Propriétés de convergence presque complète du prédicteur à noyau, Zeit. Wahrsch. verw. Gebiete 66 (1984), 441–460. Davydov, Y. A.: The invariance principle for stationary processes, Theo. Prob. Appl. 15 (1970), 487–498. Doukhan, P.: Mixing. Properties and Examples, Lecture Notes in Statistics 72, Springer Verlag, New York, 1994. Eubank, R. L., Hart, J. D., Simpson, D. G. and Stefanski, L. A.: Testing for additivity in nonparametric regression, Ann. of Stat. 23(6) (1995), 1896–1920. Fan, J., Härdle, W. and Mammen, E.: Direct estimation of low-dimensional components in additive models, Ann. of Stat. 26(3) (1998), 943–971. Hall, P. and Heyde, C. C.: Martingale Limit Theory and Its Applications, Academic Press, New York, 1981. Härdle, W. and Hall, P.: On the backfitting algorithm for additive regression models, Statistica Neerlandica 47 (1993), 43–57. Hastie, T. and Tibshirani, R.: Generalized Additive Models, Chapman & Hall, London, 1990. Liebscher, E.: Strong convergence of sums of ?-mixing random variables with applications to density estimation, Stoch. Proc. Appl. 65 (1996), 69–80. Linton, O. B.: Efficient estimation of additive nonparametric regression models, Biometrika 84 (1997), 469–473. Linton, O. B. and Härdle,W.: Estimation of additive regression models with known links, Biometrika 83 (1996), 529–540. Linton, O. B. and Nielsen, J. P.: A kernel method of estimating structured nonparametric regression based on marginal integration, Biometrika 82 (1995), 93–100. Mammen, E., Linton, O. B. and Nielsen, J. P.: The existence and asymptotic properties of a backfitting projection algorithm under weak conditions, Ann. of Stat. 27 (1999), 1443–1490. Masry, E. and Tjøstheim, D.: Additive nonlinear ARX time series and projection estimates, Econometric theory 13 (1997), 214–252. Newey, W. K.: Kernel estimation of partial means, Econometric Theory 10 (1994), 233–253. Nielsen, J. P. and Linton, O. B.: An optimization interpretation of integration and back-fitting estimators for separable nonparametric models, J. R. Statist. Soc. B 60 (1998), 217–222. Opsomer, J. D. and Ruppert, D.: On the existence and asymptotic properties of back-fitting estimators, Ann. of Stat. 25 (1997), 186–211. Rio, E.: The functional law of the iterated logarithm for stationary strongly mixing sequences, Ann. of Prob. 23 (1996), 1188–1203. Sperlich, S., Linton, O. B. and Härdle, W.: Integration and backfitting methods in additive models-finite sample properties and comparison, Test. 8 (1999), 419–458. Stone, C. J.: Additive regresssion and other nonparametric models, Ann. of Stat. 13 (1985), 698–705. Stone, C. J.: The dimensionality reduction principle for generalized additive models, Ann. of Stat. 14 (1986), 592–606. Venables, W. N. and Ripley, B.: Modern Applied Statistics with S-Plus, Springer Verlag, New-York, 1994. Wilks, D. R.: Statistical Methods in the Atmospheric Sciences: An Introduction, Academic Press, New York, 1995.