We propose an approach to the estimation of infinite sets of random vectors. The problem addressed is as follows. Given two infinite sets of random vectors, find a single estimator that estimates vectors from with a controlled associated error. A new theory for the existence and implementation of such an estimator is studied. In particular, we show that the proposed estimator is asymptotically optimal. Moreover, the estimator is determined in terms of pseudo-inverse matrices and, therefore, it always exists.
翻译:我们建议一种估算无限随机矢量的方法。 问题处理如下。 在有两组无限随机矢量的情况下, 找到一个单一的估算器, 用一个受控相关错误来估算矢量。 正在研究关于这种估计器的存在和实施的新理论。 特别是, 我们显示, 提议的估算器是非随机最佳的。 此外, 估计器是用假反向矩阵来决定的, 因此它总是存在 。