On asymptotic minimaxity of the adaptative kernel estimate of a density function

Jean Bretagnolle; Jan Mielniczuk

Annales de l'I.H.P. Probabilités et statistiques (1989)

  • Volume: 25, Issue: 2, page 143-152
  • ISSN: 0246-0203

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Bretagnolle, Jean, and Mielniczuk, Jan. "On asymptotic minimaxity of the adaptative kernel estimate of a density function." Annales de l'I.H.P. Probabilités et statistiques 25.2 (1989): 143-152. <http://eudml.org/doc/77343>.

@article{Bretagnolle1989,
author = {Bretagnolle, Jean, Mielniczuk, Jan},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {mean square error; minimax estimate; adaptative kernel estimate; data dependent bandwidth; minimax bounds; density estimates},
language = {eng},
number = {2},
pages = {143-152},
publisher = {Gauthier-Villars},
title = {On asymptotic minimaxity of the adaptative kernel estimate of a density function},
url = {http://eudml.org/doc/77343},
volume = {25},
year = {1989},
}

TY - JOUR
AU - Bretagnolle, Jean
AU - Mielniczuk, Jan
TI - On asymptotic minimaxity of the adaptative kernel estimate of a density function
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1989
PB - Gauthier-Villars
VL - 25
IS - 2
SP - 143
EP - 152
LA - eng
KW - mean square error; minimax estimate; adaptative kernel estimate; data dependent bandwidth; minimax bounds; density estimates
UR - http://eudml.org/doc/77343
ER -

References

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  2. [2] G. Benett, Probability Inequalities for the Sum of Independent Random Variables, J. Amer. Statist., Vol. 57, 1962, pp. 33-45. Zbl0104.11905
  3. [3] J. Bretagnolle and C. Huber, Estimation des densités : risque minimax, Z. Wachrscheinlichkeitstheorie und verw. Gebiete, Vol. 47, 1979, pp. 113-137. Zbl0413.62024MR523165
  4. [4] R.H. Farrell, On the Best Obtainable Rates of Convergence in Estimation of a Density Function at a Point, Ann. Math. Statist., Vol. 43, 1972, pp. 170-180. Zbl0238.62049MR300360
  5. [5] L. Gajek, On Improving Density Functions Wchich are not Bona Fide Functions, Ann. Statist., Vol. 14, 1986, pp. 1612-1618. Zbl0623.62034MR868324
  6. [6] I.A. Ibragimov and R.Z. Hasminskii, Statistical Estimation, Asymptotic Theory, Springer, 1981. Zbl0467.62026MR620321
  7. [7] E. Parzen, On Estimation of Probability Density and Mode, Ann. Math. Statist., Vol. 33, 1962, pp. 1065-1076. Zbl0116.11302MR143282
  8. [8] J. Sacks and W. Strawderman, Improvements on Linear Minimax Estimates. In Statistical Decision Theory and Related Topics 3, Vol. 2, S. S. Gupta and J. O. Berger Eds., New York, Academic Press, 1982, pp. 287-304. Zbl0574.62044MR705320
  9. [9] J. Sacks and D. Ylvisacker, Asymptotically Optimal Kernels for Density Estimation at a Point, Ann. Statist., Vol. 9, 1981, pp. 334-346. Zbl0458.62031MR606617
  10. [10] G.R. Tarell and D.W. Scott, On Improving Convergence Rates for Nonnegative Kernel Density Estimators, Ann. Statist., Vol. 8, 1980, pp. 1160-1163. Zbl0459.62031MR585714
  11. [11] M. Woodroofe, On Chosing a Delta Sequence, Ann. Math. Statist., Vol. 41, 1970, pp. 1665-1671. Zbl0229.62022MR270515
  12. [12] L.D. Brown and R.H. Farrell, A Lower Bound for the Risk in Estimating the Value of a Probability Density, Preprint Math. DtCornell University, 1987. MR1134513
  13. [13] D.L. Donoho and R.L. Liu, Geometrizing Rates of Convergence, III, Preprint Dt of Statistics, University of California, 1987. Zbl0754.62028

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