An upper bound for functions of estimators in high dimensions
提出了一个作为随机变量的上界，用于高维中估计量的函数，可帮助确定函数的收敛速度，并通过三个例子（包括高维检验和大组合投资组合的样本外方差估计）展示了其应用，允许参数个数大于样本量。
We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge faster, slower, or at the same rate as estimators depending on the behavior of the partial derivative of the function. We illustrate this via three examples. The first two examples use the upper bound for testing in high dimensions, and third example derives the estimated out-of-sample variance of large portfolios. All our results allow for a larger number of parameters, p, than the sample size, n.