Bootstrap Methods and Reproducibility Probability
Keywords:Bootstrap methods, Efron’s bootstrap method, Smoothed Efron’s bootstrap method, Reproducibility probability, Hypothesis test
Bootstrap method is one of the resampling methods, it is a powerful and computer-based method. We will use two different bootstrap methods, Efron’s bootstrap and smoothed Efron’s bootstrap. They are resampling methods but in different manner and will be explained later in this paper. The reproducibility probability is the important topic will be discussed here and will be used to compare the two bootstrap methods. It is reflecting the stability of the results of hypothesis tests, it is the probability of obtaining the same decision when repeated hypothesis test.
B. Efron. “Bootstrap methods: Another look at the jackknife.” The Annals of Statistics, vol. 7, pp.1-26, 1979.
B. Efron, R.T. Tibshirani. “Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy”. Statistical Science, vol. 1, pp 54-75,1986.
B. Efron, R.J. Tibshirani. An Introduction to the Bootstrap. Chapman and Hall, 1993.
D.B. Rubin. “The Bayesian bootstrap”. The Annals of Statistics, vol. 8, pp130-134, 1981.
D.L. Banks. “Histospline smoothing the Bayesian bootstrap.” Biometrika., vol. 4, pp. 673-684, 1988.
S. Binhimd. “Bootstrap estimate of prediction error of simple linear regression models”. American Scientific Research Journal for Engineering, Technology and Science, vol. 45, pp 274-279, 2018.
S. Binhimd, B. Almalki. “Bootstrap prediction intervals”. Applied Mathematical Science, vol. 12, pp 841-848, 2018.
J. Shao, S. Chow. “Reproducibility probability in clinical trials”. Statistics in Medicine, vol. 21, pp 1727-1742, 2002.
L. De Capitani, D. De Martini. “Reproducibility probability estimation and RP-testing for some nonparametric tests”. Entropy, vol. 18, pp 142, 2016.
W.J. Conover. Practical nonparametric statistics. Wily, 1999.
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