Optimal equivariant estimator with respect to convex loss function |
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| Institution: | 1. Boris Yeltsin Ural Federal University, Mira Str. 19, Yekaterinburg 620002, Russia;2. Gammamet Research and Production Enterprise, Tatishchev Str. 92, Yekaterinburg 620028, Russia;1. Department of Internal Medicine, Wake Forest School of Medicine, Winston-Salem, NC, United States;2. Department of Biostatistical Sciences, Wake Forest School of Medicine, Winston-Salem, NC, United States;3. Department of Epidemiology and Prevention, Wake Forest School of Medicine, Winston-Salem, NC, United States;4. Department of Health and Exercise Science, Wake Forest University, Winston-Salem, NC, United States;5. Department of Epidemiology, Colorado School of Public Health, Aurora, CO, United States;1. Department of Otology and Skull Base Surgery, Eye Ear Nose & Throat Hospital, Fudan University, Shanghai 200031, China;2. Shanghai Auditory Medical Center, Shanghai, China;3. Key Laboratory of Hearing Science, Ministry of Health, Shanghai, China;1. Ahvaz Jundishapur University of Medical Sciences, Hearing and Speech Research Center, Ahvaz, Iran;2. Iran University of Medical Sciences, Hazrat Rasoul Akram Hospital, Head and Neck Surgery, Department and Research Center of Otolaryngology, Tehran, IR, Iran;3. Iran University of Medical Sciences, Haztat Rasoul Akram Hospital, Department of Audiology, Tehran, IR, Iran;4. Ahvaz Jundishapur University of Medical Sciences, Student Research Committee, Ahvaz, Iran |
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| Abstract: | Consider a family of probability distributions which is invariant under a group of transformations. In this paper, we define an optimality criterion with respect to an arbitrary convex loss function and we prove a characterization theorem for an equivariant estimator to be optimal. We illustrate this theorem under some conditions on convex loss function. |
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