# Orthogonal series regression estimators for an irregularly spaced design

Applicationes Mathematicae (2000)

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

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topPopiński, 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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- [8] E. Rafajłowicz, Nonparametric least-squares estimation of a regression function, Statistics 19 (1988), 349-358. Zbl0649.62034
- [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.
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