HAZARD RATE ESTIMATION FOR CENSORED DATA BY WAVELET METHODS

ABSTRACT

We study the estimation of a hazard rate function based on censored data by non-linear wavelet method. We provide an asymptotic formula for the mean integrated squared error (MISE) of nonlinear wavelet-based hazard rate estimators under randomly censored data. We show this MISE formula, when the underlying hazard rate function and censoring distribution function are only piecewise smooth, has the same expansion as analogous kernel estimators, a feature not available for the kernel estimators. In addition, we establish an asymptotic normality of the nonlinear wavelet estimator.

Keywords:

• Hazard rate estimator
• Censored data
• Mean integrated square error
• Non-linear wavelet estimator
• Asymptotic normality

ACKNOWLEDGMENT

Research is partly supported by the NSF Grant DMS 0071619, the author thanks his advisor Professor Hira Koul for his constant guidance and insightful suggestion.