Abstract:

In allusion to the problem of interval estimation of small samples, an improved algorithm of interval estimation based on the idea of replicating sample from Bootstrap method into grey theory is proposed. A new sample is obtained by the idea of replicating sample from the original sample, and the grey confidence interval which satisfies grey confidence level is put forward by the grey distance measure formula. Choosing the evaluation index of interval position and interval width, the performance of intervals from the three different grey distance measure formulas is proved by the religious mathematic theorem. Theoretical analysis shows that, the condition that the distance is farthest between the grey estimation value and the least value of the sample is unnecessary and sufficient for the optimal interval position of the third method. The interrelation of interval width among the three methods is only determined by the grey confidence level. Finally, the validity of theoretical analysis results and the proposed methods are illustrated by simulation.