Adaptive estimation of a density function using beta kernels
Karine Bertin; Nicolas Klutchnikoff
ESAIM: Probability and Statistics (2014)
- Volume: 18, page 400-417
- ISSN: 1292-8100
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top- [1] B. Abdous and C.C. Kokonendji, Consistency and asymptotic normality for discrete associated-kernel estimator. Afr. Diaspora J. Math.8 (2009) 63–70. Zbl1239.62032MR2511101
- [2] K. Bertin and N. Klutchnikoff, Minimax properties of beta kernel estimators. J. Statist. Plan. Inference141 (2011) 2287–2297. Zbl1214.62038MR2775207
- [3] T. Bouezmarni and S. Van Bellegem, Nonparametric beta kernel estimator for long memory time series. Technical report (2009).
- [4] T. Bouezmarni and J.V.K. Rombouts, Nonparametric density estimation for multivariate bounded data. J. Statist. Plann. Inference140 (2010) 139–152. Zbl1178.62026MR2568128
- [5] S.X. Chen, Beta kernel estimators for density functions. Comput. Statist. Data Anal.31 (1999) 131–145. Zbl0935.62042MR1718494
- [6] S.X. Chen, Beta kernel smoothers for regression curves. Statist. Sinica10 (2000) 73–91. Zbl0970.62018MR1742101
- [7] D.B.H. Cline and J.D. Hart, Kernel estimation of densities with discontinuities or discontinuous derivatives. Statistics22 (1991) 69–84. Zbl0729.62031MR1097362
- [8] I. Dattner and B. Reiser, Estimation of distribution functions in measurement error models. Technical report (2010). Zbl06118916
- [9] L. Devroye and G. Lugosi, Combinatorial methods in density estimation. Springer Series in Statistics. Springer-Verlag, New York (2001). Zbl0964.62025MR1843146
- [10] E. Giné and R. Latała and J. Zinn, Exponential and moment inequalities for U-statistics. High dimensional probability, vol. II (Seattle, WA, 1999), Birkhäuser Boston, Boston, MA. Progr. Probab. 47 (2000) 13–38. Zbl0969.60024MR2387756
- [11] J. Gustafsson, M. Hagmann, J.P. Nielsen and O. Scaillet, Local transformation kernel density estimation of loss distributions. J. Bus. Econ. Statist.27 (2009) 161–175. MR2516437
- [12] P. Hall, Large sample optimality of least squares cross-validation in density estimation. Ann. Statist.11 (1983) 1156–1174. Zbl0599.62051MR720261
- [13] I.A. Ibragimov and R.Z. Khas’minskiĭ, More on estimation of the density of a distribution. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 108 194, 198 (1981) 72–88. Zbl0486.62039MR629401
- [14] M.C. Jones, Simple boundary correction for kernel density estimation. Statist. Comput.3 (1993) 135–146. Zbl0859.62037
- [15] C.C. Kokonendji and T.S. Kiessé, Discrete associated kernels method and extensions. Statist. Methodol.8 (2011) 497–516. Zbl1248.62052MR2834036
- [16] M. Lejeune and P. Sarda, Smooth estimators of distribution and density functions. Comput. Statist. Data Anal.14 (1992) 457–471. Zbl0937.62581MR1192215
- [17] O.V. Lepski, Asymptotically minimax adaptive estimation. I. Upper bounds. Optimally adaptive estimates. Teor. Veroyatnost. i Primenen. 36 (1991) 645–659. Zbl0738.62045MR1147167
- [18] C. McDiarmid, On the method of bounded differences, in Surveys in combinatorics (Norwich 1989), vol. 141 of London Math. Soc. Lecture Note Ser. Cambridge University Press, Cambridge (1989) 148–188. Zbl0712.05012MR1036755
- [19] H.-G. Müller, Smooth optimum kernel estimators near endpoints. Biometrika78 (1991) 521–530. Zbl1192.62108MR1130920
- [20] O. Renault and O. Scaillet, On the way to recovery: A nonparametric bias free estimation of recovery rate densities. J. Banking and Finance28 (2004) 2915–2931.
- [21] E.F. Schuster, Incorporating support constraints into nonparametric estimators of densities. Commun. Statist. − Theory Methods 14 (1985) 1123–1136. Zbl0585.62070MR797636
- [22] B.W. Silverman, Density estimation for statistics and data analysis. Monogr. Statist. Appl. Probability. Chapman & Hall, London (1986). Zbl0617.62042MR848134
- [23] Ch.J. Stone, An asymptotically optimal window selection rule for kernel density estimates. Ann. Statist.12 (1984) 1285–1297. Zbl0599.62052MR760688
- [24] Sh. Zhang and R.J. Karunamuni, On kernel density estimation near endpoints. J. Statist. Plann. Inference70 (1998) 301–316. Zbl0938.62037MR1649872
- [25] H. Victor de la Peña and S.J. Montgomery-Smith, Decoupling inequalities for the tail probabilities of multivariate U-statistics. Ann. Probab.23 (1995) 806–816. Zbl0827.60014MR1334173