New approaches to parameter estimation with finite samples

This paper proposes new methods attempting to find the unbiased parameter estimate with finite samples. The parameter estimates are obtained by solving optimization problems, and the regressors are newly formed, which may be different from the ordinary least squares method. Different criteria of the optimization problems are considered. A criterion is selected when it gets an optimal value on a random signal. The optimization problems are solved by the chosen global optimization algorithm. A number of performance measures are considered to assess the resulting estimates. The proposed method works well on the simulation example and outperforms existing methods.