A new sequential approximation method |
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| Institution: | 1. Department of Statistics, College of Arts and Sciences, Oklahoma State University, Stillwater, OK 74078, USA;2. Lilly Research Laboratories, Lilly Corporate Center, Indianapolis, IN 46285, USA;1. Department of Radiology, Suzhou Science & Technology Town Hospital, Suzhou, Jiangsu Province, China;2. Department of Radiology, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA;3. Department of Radiology, Huaian Tumor Hospital, Huai''an, Jiangsu Province, China;4. Department of Radiology, The Second Affiliated Hospital of Soochow University, Suzhou, Jiangsu Province, China;1. Centre for Learning Psychology and Experimental Psychopathology, University of Leuven, Leuven, Belgium;2. Department of Psychiatry, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA;1. Department of Consumer Science, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea;2. Department of Consumers'' Life Information, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, South Korea |
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| Abstract: | A sequential method for estimating the expected value of a random variable is proposed. Using a parametric model, the updating formula is based on the maximum likelihood estimators of the roots of the expected value function. Under certain conditions, it is demonstrated that the estimators of the roots are consistent, when a two-parameter logit model version of the procedure is used for binary data. In addition, the estimators of the logit parameters have an asymptotic normal distribution. A simulation study is performed to evaluate the effectiveness of the new method for small to medium sample sizes. Compared to other sequential approximation methods, the proposed method performed well, especially when estimating several roots simultaneously. |
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