论文标题
高维度估计器功能的上限
An Upper Bound for Functions of Estimators in High Dimensions
论文作者
论文摘要
我们为估计器在高维度中的函数提供上限作为随机变量。这种上限可能有助于确定高维度功能的收敛速率。上限随机变量可能会根据函数的部分导数的行为而更快，较慢或以与估计量相同的速率收敛。我们通过三个示例来说明这一点。前两个示例使用上限进行高维度测试，第三个示例得出了大型投资组合的估计样本外方差。我们所有的结果允许比样本量n的参数p更大。
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.
