Orthogonal series regression estimators for an irregularly spaced design

Waldemar Popiński

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 3, page 309-318
  • ISSN: 1233-7234

Abstract

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Nonparametric orthogonal series regression function estimation is investigated in the case of a fixed point design where the observation points are irregularly spaced in a finite interval [a,b]i ⊂ ℝ. Convergence rates for the integrated mean-square error and pointwise mean-square error are obtained in the case of estimators constructed using the Legendre polynomials and Haar functions for regression functions satisfying the Lipschitz condition.

How to cite

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Popiński, Waldemar. "Orthogonal series regression estimators for an irregularly spaced design." Applicationes Mathematicae 27.3 (2000): 309-318. <http://eudml.org/doc/219275>.

@article{Popiński2000,
abstract = {Nonparametric orthogonal series regression function estimation is investigated in the case of a fixed point design where the observation points are irregularly spaced in a finite interval [a,b]i ⊂ ℝ. Convergence rates for the integrated mean-square error and pointwise mean-square error are obtained in the case of estimators constructed using the Legendre polynomials and Haar functions for regression functions satisfying the Lipschitz condition.},
author = {Popiński, Waldemar},
journal = {Applicationes Mathematicae},
keywords = {convergence rates; nonparametric regression; orthogonal series estimator},
language = {eng},
number = {3},
pages = {309-318},
title = {Orthogonal series regression estimators for an irregularly spaced design},
url = {http://eudml.org/doc/219275},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Popiński, Waldemar
TI - Orthogonal series regression estimators for an irregularly spaced design
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 3
SP - 309
EP - 318
AB - Nonparametric orthogonal series regression function estimation is investigated in the case of a fixed point design where the observation points are irregularly spaced in a finite interval [a,b]i ⊂ ℝ. Convergence rates for the integrated mean-square error and pointwise mean-square error are obtained in the case of estimators constructed using the Legendre polynomials and Haar functions for regression functions satisfying the Lipschitz condition.
LA - eng
KW - convergence rates; nonparametric regression; orthogonal series estimator
UR - http://eudml.org/doc/219275
ER -

References

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  2. [2] J. Engel, A simple wavelet approach to nonparametric regression from recursive partitioning schemes, J. Multivariate Anal. 49 (1994), 242-254. Zbl0795.62034
  3. [3] R. L. Eubank, J. D. Hart and P. Speckman, Trigonometric series regression estimators with an application to partially linear models, ibid. 32 (1990), 70-83. Zbl0709.62041
  4. [4] T. Gasser and H. G. Müller, Kernel estimation of regression functions, in: Smoothing Techniques for Curve Estimation, T. Gasser and M. Rosenblatt (eds.), Lecture Notes in Math. 757, Springer, Heidelberg, 1979, 23-68. 
  5. [5] G. V. Milovanović, D. S. Mitrinović and T. M. Rassias, Topics on Polynomials: Extremal Problems, Inequalities, Zeros, World Sci., Singapore, 1994. Zbl0848.26001
  6. [6] I. Novikov and E. Semenov, Haar Series and Linear Operators, Math. Appl. 367, Kluwer, Dordrecht, 1997. Zbl0865.42024
  7. [7] E. Rafajłowicz, Nonparametric orthogonal series estimators of regression: a class attaining the optimal convergence rate in L 2 , Statist. Probab. Lett. 5 (1987), 219-224. Zbl0605.62030
  8. [8] E. Rafajłowicz, Nonparametric least-squares estimation of a regression function, Statistics 19 (1988), 349-358. Zbl0649.62034
  9. [9] L. Rutkowski, Orthogonal series estimates of a regression function with application in system identification, in: W. Grossmann et al. (eds.), Probability and Statistical Inference, Reidel, 1982, 343-347. 
  10. [10] G. Sansone, Orthogonal Functions, Interscience, New York, 1959. 
  11. [11] I. I. Sharapudinov, On convergence of least-squares estimators, Mat. Zametki 53 (1993), 131-143 (in Russian). Zbl0816.65146
  12. [12] P. K. Suetin, Classical Orthogonal Polynomials, Nauka, Moscow, 1976 (in Russian). 

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