Nonparametric regression estimates with censored data based on block thresholding method

• Published in: Journal of statistical planning and inference Vol. 143; no. 7; pp. 1150 - 1165
• Main Authors: Shirazi, E., Doosti, H., Niroumand, H.A., Hosseinioun, N.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-07-2013
• Subjects: Block thresholding; Censored data; Minimax estimation; Nonparametric regression; Rate of convergence; Censored data; Minimax estimation; Block thresholding; Rate of convergence; Nonparametric regression
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2013.01.003

Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in Li et al. (2008). The performance of proposed estimator is investigated by a numerical study.