Simultaneous likelihood-based bootstrap confidence sets for a large number of models
Simultaneous likelihood-based bootstrap confidence sets for a large number of models
复制标题
大量模型的同时基于似然的引导置信集
DOI：
10.18452/4583
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Zhilova
中科院分区：
文献类型：
--
作者：
M. Zhilova
本文研究了一个基于似然的同时置信集的构造问题。我们考虑一个同时乘数自助程序估计的似然比统计量的联合分布的分位数，并调整多重性的置信水平。理论结果表明，当样本容量n固定，最大参数维数p_max和所考虑的参数模型数K为s.t. (log K）^12 p_max^3/n很小。我们还考虑了参数模型被错误指定的情况。如果模型的误设定是显著的，则Bootstrap临界值超过真值，同时Bootstrap置信集变得保守。局部常数和局部二次回归的数值实验验证了理论结果。
The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics, and for adjusting the confidence level for multiplicity. Theoretical results state the bootstrap validity in the following setting: the sample size n is fixed, the maximal parameter dimension p_max and the number of considered parametric models K are s.t. (logK )^12 p_max^3/n is small. We also consider the situation when the parametric models are misspecified. If the models' misspecification is significant, then the bootstrap critical values exceed the true ones and the simultaneous bootstrap confidence set becomes conservative. Numerical experiments for local constant and local quadratic regressions illustrate the theoretical results.
DOI：
10.3150/10-bej272
发表时间：
2011-02
期刊：
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
影响因子：
--
作者：
Cao H;Kosorok MR
通讯作者：
Kosorok MR