标题： 关于高斯随机矩阵中最大大小的大型平均和方差分析拟合子矩阵 显示英文标题

标题： On the maximal size of Large-Average and ANOVA-fit Submatrices in a Gaussian Random Matrix

摘要： 我们研究高斯随机矩阵中特殊子矩阵的最大大小。 感兴趣的是其元素的平均值大于或等于正常数的子矩阵，以及其元素能很好地由两因素方差分析模型拟合的子矩阵。 我们确定了大平均和ANOVA拟合子矩阵的大小阈值及相关的（渐近）概率界限。 当感兴趣的矩阵和子矩阵为方阵时得到结果，在矩形情况下，当感兴趣的矩阵子矩阵具有固定的纵横比时也得到结果。 此外，我们在方阵情况下获得了大平均子矩阵大小的强区间集中结果。 模拟研究显示，在中等规模的矩阵中，观察到的大平均子矩阵大小与预测大小之间有很好的一致性。 显示英文摘要

摘要： We investigate the maximal size of distinguished submatrices of a Gaussian random matrix. Of interest are submatrices whose entries have average greater than or equal to a positive constant, and submatrices whose entries are well-fit by a two-way ANOVA model. We identify size thresholds and associated (asymptotic) probability bounds for both large-average and ANOVA-fit submatrices. Results are obtained when the matrix and submatrices of interest are square, and in rectangular cases when the matrix submatrices of interest have fixed aspect ratios. In addition, we obtain a strong, interval concentration result for the size of large average submatrices in the square case. A simulation study shows good agreement between the observed and predicted sizes of large average submatrices in matrices of moderate size.