On asymptotic minimaxity of the adaptative kernel estimate of a density function
Annales de l'I.H.P. Probabilités et statistiques, Volume 25 (1989) no. 2, p. 143-152
@article{AIHPB_1989__25_2_143_0,
     author = {Bretagnolle, Jean and Mielniczuk, Jan},
     title = {On asymptotic minimaxity of the adaptative kernel estimate of a density function},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {25},
     number = {2},
     year = {1989},
     pages = {143-152},
     zbl = {0682.62023},
     mrnumber = {1001022},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1989__25_2_143_0}
}
Bretagnolle, Jean; Mielniczuk, Jan. On asymptotic minimaxity of the adaptative kernel estimate of a density function. Annales de l'I.H.P. Probabilités et statistiques, Volume 25 (1989) no. 2, pp. 143-152. http://www.numdam.org/item/AIHPB_1989__25_2_143_0/

[1] I.S. Abramson, On Bandwidth Variation in Kernel Estimates a Square Root Law, Ann. Stat., Vol. 10, 1982, pp. 1217-1223. | MR 673656 | Zbl 0507.62040

[2] G. Benett, Probability Inequalities for the Sum of Independent Random Variables, J. Amer. Statist., Vol. 57, 1962, pp. 33-45. | Zbl 0104.11905

[3] J. Bretagnolle and C. Huber, Estimation des densités : risque minimax, Z. Wachrscheinlichkeitstheorie und verw. Gebiete, Vol. 47, 1979, pp. 113-137. | MR 523165 | Zbl 0413.62024

[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. | MR 300360 | Zbl 0238.62049

[5] L. Gajek, On Improving Density Functions Wchich are not Bona Fide Functions, Ann. Statist., Vol. 14, 1986, pp. 1612-1618. | MR 868324 | Zbl 0623.62034

[6] I.A. Ibragimov and R.Z. Hasminskii, Statistical Estimation, Asymptotic Theory, Springer, 1981. | MR 620321 | Zbl 0467.62026

[7] E. Parzen, On Estimation of Probability Density and Mode, Ann. Math. Statist., Vol. 33, 1962, pp. 1065-1076. | MR 143282 | Zbl 0116.11302

[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. | MR 705320 | Zbl 0574.62044

[9] J. Sacks and D. Ylvisacker, Asymptotically Optimal Kernels for Density Estimation at a Point, Ann. Statist., Vol. 9, 1981, pp. 334-346. | MR 606617 | Zbl 0458.62031

[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. | MR 585714 | Zbl 0459.62031

[11] M. Woodroofe, On Chosing a Delta Sequence, Ann. Math. Statist., Vol. 41, 1970, pp. 1665-1671. | MR 270515 | Zbl 0229.62022

[12] L.D. Brown and R.H. Farrell, A Lower Bound for the Risk in Estimating the Value of a Probability Density, Preprint Math. Dt Cornell University, 1987. | MR 1134513

[13] D.L. Donoho and R.L. Liu, Geometrizing Rates of Convergence, III, Preprint Dt of Statistics, University of California, 1987.