Nonlinear Confidence Estimation of Signal Parameters

Sequential analysis is applied to obtain a nonasymptotic solution for the problem of confidence estimation of a multidimensional parameter entering nonlinearly the equation of a stochastic dynamic process. The solution is obtained under nonparametric prior uncertainty regarding the distribution of the observations. A sequential design is proposed for the construction of the confidence parallelepiped of given dimensions using estimators that are asymptotically close to OLS estimators. Analytical upper bounds are derived for the mean observation time in the proposed sequential design.