Optimal designs for nonparametric estimation of zeros of regression functions

[1] BIEDERMANN, S.-DETTE, H.: Minimax optimal designs for nonparametric regres- sion-a further optimality property of the uniform distribution, in: mODa 6-Advances in Model-Oriented Design and Analysis (A. C. Atkinson et al., eds.), Puchberg/Schneeberg, Austria, 2001, Contrib. Statist., Physica-Verlag, Heidelberg, 2001, pp. 13-20.10.1007/978-3-642-57576-1_2Search in Google Scholar

[2] , Optimal designs for testing the functional form of a regression via nonparametric estimation techniques, Statist. Probab. Lett. 52 (2001), 215-224.10.1016/S0167-7152(00)00244-3Search in Google Scholar

[3] CHENG, M.-Y.-HALL, P.-TITTERINGTON, D. M.: Optimal design for curve esti- mation by local linear smoothing, Bernoulli 4 (1998), 3-14.10.2307/3318529Search in Google Scholar

[4] FARAWAY, J. J.: Sequential design for the nonparametric regression of curves and sur- faces, in: Proc. of the 22nd Symposium on the Interface, Comput. Sci. Statist., Vol. 22, Springer, 1990, pp. 104-110.10.1007/978-1-4612-2856-1_13Search in Google Scholar

[5] FEDOROV, V. V.-MONTEPIEDRA,G.-NACHTSHEIM, C. J.: Design of experiments for locally weighted regression, J. Statist. Plann. Inference 81 (1999), 363-382.10.1016/S0378-3758(99)00018-XSearch in Google Scholar

[6] GASSER, T.-M¨ULLER, H.-G.: Estimating regression functions and their derivatives by the kernel method, Scand. J. Stat. 11 (1984), 171-185.Search in Google Scholar

[7] HAINES, H.-G.: Discussion (Titterington, D. M.: Optimal design in flexible models, including feed-forward networks and nonparametric regression), Optimum Design 2000 (A. Atkinson, B. Bogacka and A. Zhigljavsky, eds.), Nonconvex Optim. Appl., Vol. 51, Kluwer, Dordrecht, 2001, pp. 272-273.Search in Google Scholar

[8] HL´AVKA, Z.: On nonparametric estimators of location of maximum, Acta Univ. Carolin. Math. Phys. 52 (2011), 5-13.Search in Google Scholar

[9] M¨ULLER, H.-G.: Boundary effects in nonparametric curve estimation models, in: 6th Symposium-COMPSTAT ’84, (T. Havr´anek, Z. ˇ Sid´ak and M. Nov´ak, eds.), Prague, 1984, Comput. Sci., Physica-Verlag, Vienna, 1984, pp. 84-89.10.1007/978-3-642-51883-6_10Search in Google Scholar

[10] , Optimal designs for nonparametric kernel regression, Statist. Probab. Lett. 2 (1984), 285-290.10.1016/0167-7152(84)90066-XSearch in Google Scholar

[11] , Kernel estimators of zeros and of location and size of extrema or regression functions, Scand. J. Stat. 12 (1985), 221-232.Search in Google Scholar

[12] M¨ULLER, W. G.: Optimal design for local fitting, J. Statist. Plann. Inference 55 (1996), 389-397.10.1016/S0378-3758(95)00197-2Search in Google Scholar

[13] NOˇZIˇCKA, F.: Calculus of variations (5th ed.), in: Pˇrehled uˇzit´e matematiky (K. Rektorys, ed.), SNTL, Prague, 1998, pp. 841-858. (In Czech)Search in Google Scholar

[14] PELIGRAD, M.: On the asymptotic normality of sequences of weak dependent random variables, J. Theoret. Probab. 9 (1996), 703-715.10.1007/BF02214083Search in Google Scholar

[15] R DEVELOPMENT CORE TEAM: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2011.Search in Google Scholar

[16] ROUSSAS, G. G.: Consistent regression estimation with fixed design points under depen- dence conditions, Statist. Probab. Lett. 8 (1989), 41-50.10.1016/0167-7152(89)90081-3Search in Google Scholar

[17] , Exponential probability inequalities with some applications, in: Statistics, Probability and Game Theory, IMS Lecture Notes Monogr. Ser., Vol. 30, Institute of Mathematical Statistics, Hayward, CA, 1996, pp. 303-319.10.1214/lnms/1215453579Search in Google Scholar

[18] ROUSSAS, G. G.-TRAN, L. T.-IOANNIDES, D. A.: Fixed design regression for time series: asymptotic normality, J. Multivariate Anal. 40 (1992), 262-291.10.1016/0047-259X(92)90026-CSearch in Google Scholar

[19] SMIRNOW, W. I.: Lehrgang der H¨oheren Mathematik, Teil IV. VEB Deutscher Verlag der Wissenschaften, Berlin, 1958.Search in Google Scholar

[20] TITTERINGTON, D. M.: Optimal design in flexible models, including feed-forward net- works and nonparametric regression, in: Optimum Design 2000 (A. Atkinson, B. Bogacka and A. Zhigljavsky, eds.), Nonconvex Optim. Appl., Vol. 51, Kluwer, Dordrecht, 2001, pp. 261-272.10.1007/978-1-4757-3419-5_23Search in Google Scholar

[21] WIENS, D. P.: Minimax robust designs and weights for approximately specified regression models with heteroscedastic errors, J. Amer. Statist. Assoc. 93 (1998), 1440-1450.10.1080/01621459.1998.10473804Search in Google Scholar