Stochastic Cramer Rao bounds for non-Gaussian signals and parameters

In minimum mean square estimation, an estimate θ´ of the random parameter vector θ is obtained from an input vector y. We develop bounds on the variances of elements of θ´-θ for the case where input signal vector y and the parameter vector θ are non-Gaussian. First, we use linear transformations to obtain a new parameter vector φ from θ and a new input vector x from y. These new vectors are approximately Gaussian because of the central limit theorem, so stochastic Cramer-Rao bounds on the variance of φ´-φ are tight. Lastly, bounds on variances of elements of θ-θ are obtained