Summary
Boundary effects disturb nonparametric curve estimates, especially of derivatives, near the boundaries of the support of the curve. Modifications of estimates near the boundaries are necessary in order to obtain global asymptotic results as well as a satisfying finite sample behavior. We describe such modifications exhibiting different degrees of smoothness and derive the rate of a.s. convergence of the supremal deviation of nonparametric kernel regression, supremum taken over the deviation on the whole interval of support of the function to be estimated. A “reference kernel method” is proposed which allows the construction of modified kernels of different degrees of smoothness. This method requires substantially less computations than previous approaches.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cheng, K. F., Lin, P. E. (1981). Nonparametric estimation of a regression function. Z. Wahrscheinlichkeitstheorie vera. Geb. 57, 223–233
Gasser, Th., Müller, H. G. (1979). Kernel estimation of regression functions. Smoothing techniques for curve estimation, Proceedings Heidelberg 1979, Lecture notes in mathematics 757, 23 – 68
Gasser, Th., Müller, H. G. (1984). Estimating regression functions and their derivatives by the kernel method.Scand.J.Statist., in press
Hall, P. (1981). On trigonometric series estimates of densities. Ann. Statist. 9, 683–685
Hominal, P., Deheuvels, P. (1979). Estimation non-paramétrique de la densité compte-tenu d’informations sur le support. Revue de Statistique Appliqueé 27, 47 – 59
Lamperti, J. (1966). Probability. New York
Müller, H. G. (1984). Smooth optimum kernel estimators of regression curves, densities and modes. Ann. Statist. 12, in press
Priestley, M. B., Chao, M. T. (1972). Nonparametric function fitting. J. Royal Statist. Soc. B34, 385–392
Rice, J. (1983). Boundary modification for kernel regression. Pre- print, University of California, San Diego
Rice, J., Rosenblatt, M. (1983). Smoothing splines: regression derivatives, and deconvolution. Ann. Statist. 11, 141–156
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Müller, HG. (1984). Boundary Effects in Nonparametric Curve Estimation Models. In: Havránek, T., Šidák, Z., Novák, M. (eds) Compstat 1984. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-51883-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-51883-6_10
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7051-0007-7
Online ISBN: 978-3-642-51883-6
eBook Packages: Springer Book Archive