Bias and mean square error properties of general estimators

This paper uses high order sensitivity analysis for the determination of bias and mean square errors of general estimators with finite and infinite samples. The errors in maximum likelihood estimates are analyzed in detail. It is Shown that in finite data, the maximum likelihood estimates may be substantially biased and possess mean square errors substantially higher than Cramer-Rao bounds. The errors caused by inaccurate models are determined, leading to a technique for selection of parameters in practical estimation problems.