Bootstrap模型平均置信区间
Model-Averaged Bootstrap Confidence Interval
摘要: 模型平均作为能够解决模型不确定性的统计推断方法越来越受欢迎，模型平均应用也从点估计扩展到区间估计。目前模型平均置信区间常用方法包括Wald区间和MATA-Wald区间，这些区间都是在参数估计的分布渐近正态的情况下构建的，所以这两种方法在拟合正态数据时效果是非常好的。在本文中，我们将参数估计的Bootstrap分布来近似其真实分布，进而提出了Bootstrap模型平均置信区间，并对这3种方法分别在正态数据和偏态数据的模型下的表现进行模拟比较。模拟结果表明在正态数据的模型下，Bootstrap模型平均置信区间在上错误率和覆盖率方面仅略差于MATA区间。在偏态数据的模型下，百分位数Bootstrap模型平均置信区间的覆盖率要优于Wald区间和MATA区间，并且提供了较好的错误率，特别是上错率，都更接近名义水平。所以Boorstrap区间表现出很好的适应性。
Abstract: Model averaging is becoming more and more popular as a statistical inference method to solve model uncertainty, and the application of model averaging is also extended from point estimation to interval estimation. At present, the common methods of model averaged confidence interval include Wald interval and MATA-Wald interval. These intervals are constructed under the condition that the distribution of parameter estimation is asymptotically normal. Therefore, these two methods are very good in fitting normal data. In this paper, the bootstrap distribution of parameter estimation was approximated to the real distribution, and then the model-averaged bootstrap interval was proposed. The performance of the three methods under normal and skewered data models was simulated and compared respectively. The simulation results show that the model-averaged bootstrap interval is only slightly worse than that of the MATA model in the upper error rate and coverage under the normal data model, Under the model with skewed data, the coverage of the model-averaged bootstrap interval is better than that of the Wald interval and the MATA interval, and it also provides a better error rate, especially the upper error rate, which is closer to the nominal level. So the bootstrap interval shows good adaptability.
文章引用：郭庆光, 李新民. Bootstrap模型平均置信区间[J]. 应用数学进展, 2021, 10(11): 3802-3810. https://doi.org/10.12677/AAM.2021.1011403

参考文献

[1] Chatfield, C. (1995) Model Uncertainty, Data Mining and Statistical Inference. Journal of the Royal Statistical Society: Series A, 158, 419-466. [Google Scholar] [CrossRef] 
[2] Wasserman, L. (2000) Bayesian Model Selection and Model Averaging. Journal of Mathematical Psychology, 44, 92-107. [Google Scholar] [CrossRef] [PubMed]
[3] Wang, H. and Zhou, S.Z. (2013) Interval Estimation by Frequentist Model Averaging. Communications in Statistics, 42, 4342-4356. [Google Scholar] [CrossRef] 
[4] Buckland, S.T., Burnham, K.P. and Augustin. N.H. (1997) Model Selection: an Integral Part of Inference. Biometrics, 53, 603-618. [Google Scholar] [CrossRef] 
[5] Hjort, N.L. and Claeskens, G. (2003) Frequentist Model Average Estimators. Journal of the American Statistical Association, 98, 879-899. [Google Scholar] [CrossRef] 
[6] Burnham, K. and Anderson, D. (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd Edition, Springer, New York.
[7] Buckland, S.T., Burnham, K.P. and Augustin, N.H. (1997) Model Selection: An Integral Part of Inference. Biometrics, 53, 603-618. [Google Scholar] [CrossRef] 
[8] Turek, D. and Fletcher, D. (2012) Model-Averaged Wald Confidence Intervals. Computational Statistics and Data Analysis, 56, 2809-2815. [Google Scholar] [CrossRef] 
[9] Fletcher, D. and Turek, D. (2012) Model-Averaged Profile Likelihood Intervals. Journal of Agricultural, Biological, and Environmental Statistics, 17, 38-51. [Google Scholar] [CrossRef] 
[10] Kabaila, P., Welsh, A. and Abeysekera, W. (2016) Model-Averaged Confidence Intervals. Scandinavian Journal of Statistics, 43, 35-48. [Google Scholar] [CrossRef] 
[11] Kabaila, P. (2018) On the Minimum Coverage Probability of Model Averaged Tail Area Confidence Intervals. Canadian Journal of Statistics, 46, 279-297. [Google Scholar] [CrossRef] 
[12] Kabaila, P., Welsh, A.H. and Mainzer, R. (2017) The Performance of Model Averaged Tail Area Confidence Intervals. Communications in Statistics-Theory and Methods, 46, 10718-10732. [Google Scholar] [CrossRef] 
[13] Yu, W., Xu, W. and Zhu, L. (2014) Transformation-Based Model-Averaged Tail Area Inference. Computational Statistics, 29, 1713-1726. [Google Scholar] [CrossRef] 

为你推荐