Bounds on the Bias of Signal Parameter Estimators

Any estimator which is constrained to take values in a finite range is, in general, biased. Many times the bias is unknown; furthermore, in some cases the bias may become the main contributor to the mean square enor of an estimator. This paper derives upper and lower bounds on the bias of a finite-range, signal parameter estimator. 1.1 Introduction Let the parameter be denoted by a and let a take values in [--a, a]. We refer to 2a as the a pnori range (or space) of a. We assume that there exists probabilistic mapping from the parameter space to an observation space, that is, a probability law that governs the effect of a on the observation.1 This probability law will be referred to as the "channel." After observing the "outcome" which is a point in the observation space, we estimate the value of a. Let this estimate be denoted by a. Clearly, a is a random variable. We assume, throughout this paper, that a takes values in [--A, A]. Let the bias be defined (1)