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2000 | 27 | 3 | 309-318
Tytuł artykułu

Orthogonal series regression estimators for an irregularly spaced design

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
27
Numer
3
Strony
309-318
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-27
poprawiono
2000-01-05
Twórcy
  • Department of Standards, Central Statistical Office, Al. Niepodległości 208, 00-925 Warszawa, Poland
Bibliografia
  • [1] T. T. Cai and L. D. Brown, Wavelet estimation for samples with random uniform design, Statist. Probab. Lett. 42 (1999), 313-321.
  • [2] J. Engel, A simple wavelet approach to nonparametric regression from recursive partitioning schemes, J. Multivariate Anal. 49 (1994), 242-254.
  • [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.
  • [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] G. V. Milovanović, D. S. Mitrinović and T. M. Rassias, Topics on Polynomials: Extremal Problems, Inequalities, Zeros, World Sci., Singapore, 1994.
  • [6] I. Novikov and E. Semenov, Haar Series and Linear Operators, Math. Appl. 367, Kluwer, Dordrecht, 1997.
  • [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.
  • [8] E. Rafajłowicz, Nonparametric least-squares estimation of a regression function, Statistics 19 (1988), 349-358.
  • [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] G. Sansone, Orthogonal Functions, Interscience, New York, 1959.
  • [11] I. I. Sharapudinov, On convergence of least-squares estimators, Mat. Zametki 53 (1993), 131-143 (in Russian).
  • [12] P. K. Suetin, Classical Orthogonal Polynomials, Nauka, Moscow, 1976 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv27i3p309bwm
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