On the degrees of freedom of reduced-rank estimators in multivariate regression.
On the degrees of freedom of reduced-rank estimators in multivariate regression.
复制标题
在多元回归中降低级别估计器的自由度。
作者：
Mukherjee A;Chen K;Wang N;Zhu J
在Stein的无偏风险估计的框架下，我们研究了一类一般的多元回归降维估计的有效自由度。给出了一种有限样本精确无偏估计，它允许用最小二乘解的门限奇异值表示的闭合形式，因此易于计算。结果继续适用于高维设置，其中预测器和响应维度都可能大于样本量。推导出的解析形式方便了理论性质的研究，并为自由度的经验行为提供了新的见解。特别地，我们考察了所提出的估计量和常用的朴素估计量之间的区别和联系。仿真研究和数据实例表明，所提出的估计器能够有效和准确地进行预测风险估计和模型选择。
We study the effective degrees of freedom of a general class of reduced-rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation. A finite-sample exact unbiased estimator is derived that admits a closed-form expression in terms of the thresholded singular values of the least-squares solution and hence is readily computable. The results continue to hold in the high-dimensional setting where both the predictor and the response dimensions may be larger than the sample size. The derived analytical form facilitates the investigation of theoretical properties and provides new insights into the empirical behaviour of the degrees of freedom. In particular, we examine the differences and connections between the proposed estimator and a commonly-used naive estimator. The use of the proposed estimator leads to efficient and accurate prediction risk estimation and model selection, as demonstrated by simulation studies and a data example.