On least squares estimation of Fourier coefficients and of the regression function

Waldemar Popiński

Applicationes Mathematicae (1993)

  • Volume: 22, Issue: 1, page 91-102
  • ISSN: 1233-7234

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Popiński, Waldemar. "On least squares estimation of Fourier coefficients and of the regression function." Applicationes Mathematicae 22.1 (1993): 91-102. <http://eudml.org/doc/219086>.

@article{Popiński1993,
abstract = {},
author = {Popiński, Waldemar},
journal = {Applicationes Mathematicae},
keywords = {Fourier series; consistent estimator; least squares method; regression; mean square prediction error; nonparametric regression; nonparametric function fitting; limits in probability; complete orthonormal system},
language = {eng},
number = {1},
pages = {91-102},
title = {On least squares estimation of Fourier coefficients and of the regression function},
url = {http://eudml.org/doc/219086},
volume = {22},
year = {1993},
}

TY - JOUR
AU - Popiński, Waldemar
TI - On least squares estimation of Fourier coefficients and of the regression function
JO - Applicationes Mathematicae
PY - 1993
VL - 22
IS - 1
SP - 91
EP - 102
AB -
LA - eng
KW - Fourier series; consistent estimator; least squares method; regression; mean square prediction error; nonparametric regression; nonparametric function fitting; limits in probability; complete orthonormal system
UR - http://eudml.org/doc/219086
ER -

References

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  1. [1] H. Akaike, A new look at the statistical model identification, IEEE Trans. Automat. Control AC-19 (1974), 716-723 Zbl0314.62039
  2. [2] Y. S. Chow and H. Teicher, Probability Theory, Independence, Interchangeability, Martingales, Springer, Heidelberg, 1978 
  3. [3] C. L. Mallows, Some comments on C_p, Technometrics 15 (1973), 661-675 
  4. [4] B. T. Polyak and A. B. Tsybakov, Asymptotic optimality of the C_p criterion in projection type estimation of a regression function, Teor. Veroyatnost. i Primenen. 35 (1990), 305-317 (in Russian) 
  5. [5] E. Rafajłowicz, Nonparametric least-squares estimation of a regression function, Statistics 19 (1988), 349-358 Zbl0649.62034
  6. [6] G. Sansone, Orthogonal Functions, Interscience, New York, 1959. 

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