Asymmetric kernel regression

Kernel regression is one model that has been applied to explain or design radial-basis neural networks. Practical application of the kernel regression method has shown that bias errors caused by the boundaries of the data can seriously effect the accuracy of this type of regression. This paper investigates the correction of boundary error by substituting an asymmetric kernel function for the symmetric kernel function at data points close to the boundary. The asymmetric kernel function allows a much closer approach to the boundary to be achieved without adversely effecting the noise-filtering properties of the kernel regression.

[1]  S. Loukas,et al.  Nonparametric Estimation of Probability Densities and Regression Curves. , 1991 .

[2]  E. Bolinder.  The Fourier integral and its applications , 1963 .

[3]  D. W. Scott,et al.  Nonparametric Estimation of Probability Densities and Regression Curves , 1988 .

[4]  E. Nadaraya.  On Estimating Regression , 1964 .

[5]  Donald F. Specht,et al.  A general regression neural network , 1991, IEEE Trans. Neural Networks.

[6]  Jianqing Fan,et al.  Variable Bandwidth and Local Linear Regression Smoothers , 1992 .

[7]  J. Marron,et al.  Transformations to reduce boundary bias in kernel density estimation , 1994 .

[8]  H. Müller,et al.  Kernel estimation of regression functions , 1979 .

[9]  Peter Hall,et al.  A Geometrical Method for Removing Edge Effects from Kernel-Type Nonparametric Regression Estimators , 1991 .

[10]  Daniel G. Sbarbaro-Hofer,et al.  Applications of radial basis network technology to process control , 2000, IEEE Trans. Control. Syst. Technol..

[11]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[12]  James Stephen Marron,et al.  Choosing a Kernel Regression Estimator , 1991 .

[13]  Peter Hall,et al.  Integrated Square Error Properties of Kernel Estimators of Regression Functions , 1984 .

[14]  Matthew P. Wand,et al.  Kernel Smoothing , 1995 .

[15]  F. L. Crosswy,et al.  Signal Conditioning Electronics for a Laser Vector Velocimeter , 1973 .

[16]  E. Nadaraya.  On Non-Parametric Estimates of Density Functions and Regression Curves , 1965 .

[17]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[18]  G. S. Watson,et al.  Smooth regression analysis , 1964 .

[19]  H.K. Kim.  Filtering in the time and frequency domains , 1978, Proceedings of the IEEE.

[20]  M. Priestley,et al.  Non‐Parametric Function Fitting , 1972 .

[21]  Peter Hall,et al.  On Pseudodata Methods for Removing Boundary Effects in Kernel Density Estimation , 1996 .

[22]  M. C. Jones,et al.  An Improved Estimator of the Density Function at the Boundary , 1999 .

[23]  Anthony Zaknich,et al.  Introduction to the modified probabilistic neural network for general signal processing applications , 1998, IEEE Trans. Signal Process..