Estimation of a k − monotone density , part 3 : limiting Gaussian versions of the problem ; invelopes and envelopes

@inproceedings{Balabdaoui2004EstimationOA,
  title={Estimation of a k − monotone density , part 3 : limiting Gaussian versions of the problem ; invelopes and envelopes},
  author={Fadoua Balabdaoui and J. A. Wellner},
  year={2004}
}
Let k be a positive integer. The limiting distribution of the nonparametric maximum likelihood estimator of a k−monotone density is given in terms of a smooth stochastic process Hk described as follows: (i) Hk is everywhere above (or below) Yk, the k− 1 fold integral of two-sided standard Brownian motion plus (k!/(2k)!)t2k when k is even (or odd). (ii) H(2k−2) k is convex. (iii) Hk touches Yk at exactly those points where H(2k−2) k has changes of slope. We show that Hk exists if a certain… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 26 references

Weak Convergence and Empirical Processes

  • A. W. van der Vaart, J. A. Wellner
  • 1996
Highly Influential
8 Excerpts

Cube root asymptotics

  • J. Kim, D. Pollard
  • Ann. Statist. 18, 191-219. Kopotun, K. and…
  • 1990
Highly Influential
20 Excerpts

Estimating a monotone density

  • P. Groeneboom
  • Proceedings of the Berkeley Conference in Honor…
  • 1985
Highly Influential
13 Excerpts

Radial positive definite functions generated by Euclid’s hat

  • T. Gneiting
  • J. Multivariate Analysis 69, 88 - 119.
  • 1999
Highly Influential
6 Excerpts

Constructive Approximation

  • R. A. DeVore, G. G. Lorentz
  • SpringerVerlag, Berlin.
  • 1993
Highly Influential
7 Excerpts

Bounding the error in spline interpolation

  • C. de Boor
  • SIAM Rev. 16,
  • 1974
Highly Influential
4 Excerpts

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