论文标题
在高维度下模型错误指定下的似然比测试
Likelihood ratio tests under model misspecification in high dimensions
论文作者
论文摘要
我们研究了大型块 - 基因协方差矩阵的可能性比测试，其在无原假设下的块数量越来越多。尽管到目前为止仅研究了正常人群的似然比统计量，但我们确定其渐近行为在更大的分布类别下是不变的。这意味着反对模型错误指定的鲁棒性，这在高维度中很常见。为了证明我们方法的灵活性，我们还建立了模型不确定性下许多大型样品协方差矩阵的相等性的对数似然比测试统计统计统计量的渐近正态性。对于此统计数据，与正常情况相比，需要对中心项进行微妙的调整。对心理学数据集的模拟研究和分析强调了我们发现的有用性。
We investigate the likelihood ratio test for a large block-diagonal covariance matrix with an increasing number of blocks under the null hypothesis. While so far the likelihood ratio statistic has only been studied for normal populations, we establish that its asymptotic behavior is invariant under a much larger class of distributions. This implies robustness against model misspecification, which is common in high-dimensional regimes. Demonstrating the flexibility of our approach, we additionally establish asymptotic normality of the log-likelihood ratio test statistic for the equality of many large sample covariance matrices under model uncertainty. For this statistic, a subtle adjustment to the centering term is needed compared to normal case. A simulation study and an analysis of a data set from psychology emphasize the usefulness of our findings.
