Higher-order accuracy of multiscale-double bootstrap for testing regions
Higher-order accuracy of multiscale-double bootstrap for testing regions
复制标题
测试区域的多尺度双引导的高阶精度
DOI：
10.1016/j.jmva.2014.05.007
复制
发表时间：
2014
影响因子：
1.6
通讯作者：
Hidetoshi Shimodaira
中科院分区：
文献类型：
--
作者：
T. Hasegawa;T. Mori;R. Yamaguchi;S. Miyano;T. Akutsu;Hidetoshi Shimodaira
我们认为假设检验的零假设被表示为一个任意形状的区域中的参数空间。我们通过计算零假设在bootstrap重复中成立的次数来计算近似p值。这种频率被称为自举概率，广泛用于进化生物学中，但在文献中经常被报道为有偏见。基于Bootstrap置信区间的渐近理论，已有一些新的尝试通过Bootstrap概率来调整偏倚，而无需直接访问参数值。一种这样的尝试是双自举，其通过自举概率来调整偏差。另一个新的尝试是多尺度自举，它类似于m-out-of-n自举，但非常不寻常地将自举概率外推到m=− n。在本文中，我们同时使用这两种尝试，并称之为多尺度双引导的新过程。通过专注于多元正态模型，我们调查高阶渐近四阶精度。区域几何在渐近理论中起着重要的作用。在文献中已知，区域的边界表面的曲率决定自助概率的偏差。我们发现，“曲率的曲率”决定了双重自助法的剩余偏差。多尺度bootstrap消除了这些偏差。多尺度双重自助是四阶精度的，覆盖概率误差仅为O（n− 2），并且它对用于从零分布生成自助重复的参数估计的计算误差具有鲁棒性。
We consider hypothesis testing for the null hypothesis being represented as an arbitrary-shaped region in the parameter space. We compute an approximate p-value by counting how many times the null hypothesis holds in bootstrap replicates. This frequency, known as bootstrap probability, is widely used in evolutionary biology, but often reported as biased in the literature. Based on the asymptotic theory of bootstrap confidence intervals, there have been some new attempts for adjusting the bias via bootstrap probability without direct access to the parameter value. One such an attempt is the double bootstrap which adjusts the bias by bootstrapping the bootstrap probability. Another new attempt is the multiscale bootstrap which is similar to the m-out-of-n bootstrap but very unusually extrapolating the bootstrap probability to m=− n. In this paper, we employ these two attempts at the same time, and call the new procedure as multiscale-double bootstrap. By focusing on the multivariate normal model, we investigate higher-order asymptotics up to fourth-order accuracy. Geometry of the region plays important roles in the asymptotic theory. It was known in the literature that the curvature of the boundary surface of the region determines the bias of bootstrap probability. We found out that the “curvature of curvature” determines the remaining bias of double bootstrap. The multiscale bootstrap removes these biases. The multiscale-double bootstrap is fourth order accurate with coverage probability erring only O (n− 2), and it is robust against computational error of parameter estimation used for generating bootstrap replicates from the null distribution.