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On the block thresholding wavelet estimators with censored data

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  • Li, Linyuan

Abstract

We consider block thresholding wavelet-based density estimators with randomly right-censored data and investigate their asymptotic convergence rates. Unlike for the complete data case, the empirical wavelet coefficients are constructed through the Kaplan-Meier estimators of the distribution functions in the censored data case. On the basis of a result of Stute [W. Stute, The central limit theorem under random censorship, Ann. Statist. 23 (1995) 422-439] that approximates the Kaplan-Meier integrals as averages of i.i.d. random variables with a certain rate in probability, we can show that these wavelet empirical coefficients can be approximated by averages of i.i.d. random variables with a certain error rate in L2. Therefore we can show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes , p>=2, q>=1 and nearly optimal convergence rates when 1

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  • Li, Linyuan, 2008. "On the block thresholding wavelet estimators with censored data," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1518-1543, September.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:8:p:1518-1543
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    References listed on IDEAS

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    1. A. Antoniadis & G. Grégoire & G. Nason, 1999. "Density and hazard rate estimation for right‐censored data by using wavelet methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 63-84.
    2. Chicken, Eric & Cai, T. Tony, 2005. "Block thresholding for density estimation: local and global adaptivity," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 76-106, July.
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    1. Fabienne Comte & Gwennaelle Mabon & Adeline Samson, 2017. "Spline regression for hazard rate estimation when data are censored and measured with error," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(2), pages 115-140, May.
    2. Li, Linyuan, 2015. "Nonparametric adaptive density estimation on random fields using wavelet method," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 346-355.
    3. Fabienne Comte & Adeline Samson & Julien J. Stirnemann, 2018. "Hazard estimation with censoring and measurement error: application to length of pregnancy," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 338-359, June.

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