MEMBERSHIP SET ESTIMATORS - SIZE, OPTIMAL INPUTS, COMPLEXITY AND RELATIONS WITH LEAST-SQUARES

In this paper, we study some fundamental properties of the membership set estimators, First, the size of the membership set S-N is derived i f the noise is bounded by epsilon but otherwise unknown, Second, in th e case when the noise is an independent and identically distributed ra ndom variable in the interval [-epsilon, epsilon], the probability dis tribution of the size of S-N is also obtained. We then derive optimali ty conditions on the input in order to minimize the size of this set, Finally, we study the relations between least squares and membership s et estimators and we obtain necessary and sufficient conditions under which the least squares estimate lies in S-N.