A decision theoretic approach to parameter estimation

A decision theoretic approach to estimation of unknown random and nonrandom parameters from a linear measurements model is proposed, when the a priori statistics are incomplete and only a small number of data points are available. The unknown statistics are partially characterized by considering two regions in the measurement space, namely, good and bad data regions and constraining the partial probability, the partial covariance, or the combination thereof of the measurements. The random parameter is assumed to be Gaussian variable with known mean and known covariance. Choosing the minimum covariance criterion, the min-max estimator is found to be soft-limiter or tangent type nonlinear function depending upon the a priori statistic available. The estimator for the unknown nonrandom parameter is obtained from the root of some function of the residuals, the function being obtained by minimizing the error covariance. The estimator obtained is similar to a random parameter case.