Grey Distance Information Approach for Parameter Estimation of Small Samples

Parameter estimation of small samples is a valuable research problem in various test domains. Because of the complexity in determining the probability distribution, it is difficult to use a traditional probability theory to process the samples and assess the degree of uncertainty. Based on the grey relational theory and the norm theory, the grey distance information approach for small-sample processing is proposed. The correlative problems, including the definitions and the characteristics of the grey distance information quantity and the average grey distance information quantity, the point estimation and the confidence interval estimation algorithm, and the acceptance and rejection criteria of the samples, are also proposed. In addition, the information whitening ratio is introduced to select the weight algorithm and to compare the different sample sets. Several examples are given to demonstrate the application of the proposed approach. The examples show that the proposed approach, which has no demand for the probability distribution of small samples, is feasible and effective.