Study on grey parameter estimation approach of small samples

Abstract

Parameter estimation of small samples is a valuable research problem in various research domains. Traditional statistical parameter estimation approach needs to seek the distribution regularity of samples under some assumptions. But the assumptions usually bring new error to the parameter estimation value and make the reliability of the parameter estimation lower. Firstly, from the view of the topology of the sample space and the distances between samples, a new non-statistical parameter estimation approach and a grey parameter estimation approach based on grey theory and norm were proposed. Secondly, the correlative model and algorithms, including the definitions of the grey distance measure and grey relation entropy, were introduced. And the grey parameter estimation approach was compared with traditional statistical parameter estimation approach, too. Finally, the parameter estimation examples by the proposed approach were given. The simulations show that the approach is feasible and effective.