Mathematical proof of the third order accuracy of the speedy double bootstrap method |
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Authors: | Aizhen Ren Takashi Ishida Yutaka Akiyama |
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Affiliation: | 1. College of Science, Inner Mongolia Agricultural University, Huhhot, China;2. ren_az74@yahoo.co.jp;4. Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan |
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Abstract: | AbstractIn our previous research, we proposed a speedy double bootstrap method for assessing the reliability of statistical models with maximum log-likelihood criterion. It can provide 3rd order accurate probabilities. In this study, our focus switches to the mathematical proof. We propose an alternative proof of the third order accuracy in the context of the multivariate normal model. Our proof is based on tube formula differential geometric methodology and an Taylor series approach to the asymptotic analysis of the bootstrap method. |
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Keywords: | Speedy double bootstrap tube coordinate third order accurate |
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