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Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations
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Han-Ying Liang
Published/Copyright:
September 25, 2009
Summary
In this paper, we discuss the global L2 error of the nonlinear wavelet estimators of the density function in the Besov space Bspq, when the survival times form a stationary α-mixing sequence, and prove that the nonlinear wavelet estimators can achieve the optimal rate of convergence, which is similar to the result of Donoho et al. (1996). Also, the optimal convergence rates of the nonlinear wavelet estimators of the hazard rate function in the Besov space Bspq are considered, which had not been discussed by Donoho et al. (1996) for complete data in the i.i.d. case.
Keywords: nonlinear wavelet estimator; right censoring; density estimator; hazard rate estimator; α-mixing sequence
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Published Online: 2009-09-25
Published in Print: 2005-03-01
© R. Oldenbourg Verlag, München
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- Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations
- Empirical Bayes estimation by wavelet series
- Duality theory for optimal investments under model uncertainty
- Qualitative stability of stochastic programs with applications in asymptotic statistics
Keywords for this article
nonlinear wavelet estimator;
right censoring;
density estimator;
hazard rate estimator;
α-mixing sequence
Articles in the same Issue
- Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations
- Empirical Bayes estimation by wavelet series
- Duality theory for optimal investments under model uncertainty
- Qualitative stability of stochastic programs with applications in asymptotic statistics
