WEAK AND STRONG UNIVERSAL CONSISTENCY OF SEMI-RECURSIVE KERNEL AND PARTITIONING REGRESSION ESTIMATES

Results are presented conceming semi-recursive kemel and partitioning estimates for a regression function. Under some mild conditions on the kemel, on the bandwidth and on the partitions the weak and strong consistencies are shown without any condition on the underlying distribution.

[1]  K. Knopp Infinite sequences and series , 1957 .

[2]  T. Broadbent Measure and Integral , 1957, Nature.

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

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

[5]  Charles T. Wolverton,et al.  Recursive Estimates of Probability Densities , 1969, IEEE Transactions on Systems Science and Cybernetics.

[6]  H. Robbins,et al.  A CONVERGENCE THEOREM FOR NON NEGATIVE ALMOST SUPERMARTINGALES AND SOME APPLICATIONS**Research supported by NIH Grant 5-R01-GM-16895-03 and ONR Grant N00014-67-A-0108-0018. , 1971 .

[7]  E. Stein,et al.  Introduction to Fourier Analysis on Euclidean Spaces. , 1971 .

[8]  Hajime Yamato,et al.  SEQUENTIAL ESTIMATION OF A CONTINUOUS PROBABILITY DENSITY FUNCTION AND MODE , 1971 .

[9]  I. Ahmad,et al.  NONPARAMETRIC SEQUENTIAL ESTIMATION OF A MULTIPLE REGRESSION FUNCTION , 1976 .

[10]  C. J. Stone,et al.  Consistent Nonparametric Regression , 1977 .

[11]  L. Devroye,et al.  Distribution-Free Consistency Results in Nonparametric Discrimination and Regression Function Estimation , 1980 .

[12]  C. Spiegelman,et al.  Consistent Window Estimation in Nonparametric Regression , 1980 .

[13]  L. Devroye,et al.  On the L1 convergence of kernel estimators of regression functions with applications in discrimination , 1980 .

[14]  L. Devroye On the Almost Everywhere Convergence of Nonparametric Regression Function Estimates , 1981 .

[15]  Adam Krzyzak,et al.  Distribution-free consistency of a nonparametric kernel regression estimate and classification , 1984, IEEE Trans. Inf. Theory.

[16]  W. Greblicki,et al.  Necessary and sufficient consistency conditions for a recursive kernel regression estimate , 1987 .

[17]  L. Devroye,et al.  CONVERGENCE OF THE KERNEL REGRESSION ESTIMATE * , 1989 .

[18]  L. Györfi Universal Consistencies of a Regression Estimate for Unbounded Regression Functions , 1991 .

[19]  Adam Krzyzak,et al.  Global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation , 1992, IEEE Trans. Inf. Theory.

[20]  L. Györfi,et al.  On the strong universal consistency of a recursive regression estimate by Pál Révész , 1997 .