Statistical Analysis for Censored Data and Long Memory Data Using Wavelet Method

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The wavelet method is widely used in many applications, such as signal processing, medical imaging, pattern recognition, and many others. In this project, the investigator focuses on applications of wavelet methods to analyze censored data and estimate non-parametric curves with long range dependence data. The project is to establish asymptotically optimal and robust estimators for nonparametric function estimations with censored data and long memory data. It extends beyond the standard Gaussian error assumption to non-Gaussian error structures, with long memory. This project studies a class of important statistical tools called 'wavelet methods' for censored and long memory data. It has wide range of applications in signal process, medical imaging, pattern recognition and many others. It will provide more reliable and flexible methods to examine unknown structures of the underlying functional relationship between different features encountered in many applications.