Interpolation Estimator for Infinite Sets of Random Vectors

TL;DR

This paper introduces an interpolation estimator for infinite sets of random vectors, providing a theoretical foundation for its existence, optimality, and practical implementation using pseudo-inverse matrices.

Contribution

It develops a new theory for estimating infinite sets of random vectors, demonstrating the estimator's existence, asymptotic optimality, and implementation via pseudo-inverses.

Findings

Estimator always exists due to pseudo-inverse formulation

Proven asymptotic optimality of the estimator

Theoretical framework for infinite set estimation

Abstract

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.