Abstract

The optimal parameter estimation problem is considered. The optimization problem is solved in the general problem statement. A model-free approach is applied and supposes no knowledge of the model that the parameter to be estimated belongs to. Optimality of the considered estimators in the sense of a special type risk function is established. The considered risk function makes it possible to optimize the asymptotic variances of the estimators and is used for sample size estimation. Applications for optimization of the truncated parameter estimators of heavy-tailed indexes of distributions, such as Pareto type, Cauchy, and log-gamma, are presented. A class of these estimators is introduced having guaranteed accuracy based on a sample of fixed size. Simulation results confirm theoretical results.

摘要

考虑最佳参数估计问题。优化问题在一般问题说明中得以解决。应用无模型方法，并且假定不知道要估计的参数所属的模型。建立了在特殊类型风险函数意义上考虑的估计量的最优性。所考虑的风险函数可以优化估计量的渐近方差，并用于样本量估计。提出了优化重尾分布索引的截断参数估计器（例如Pareto类型，Cauchy和log-gamma）的应用。基于固定大小的样本，引入了一类具有保证准确性的估计量。仿真结果证实了理论结果。