On best asymptotic confidence intervals for parameters of stochastic processes. (English) Zbl 0745.62027

Summary: This paper is concerned with the size of confidence intervals for parameters of stochastic processes based on limit laws with two competing normalizations, one producing asymptotic normality and the other asymptotic mixed normality. It is shown that, in a certain sense, the interval based on asymptotic normality is preferable on average. Applications to estimation of parameters in nonergodic stochastic processes and to estimation of steady-state parameters in a simulation are given to illustrate the theory.


62F25 Parametric tolerance and confidence regions
62M09 Non-Markovian processes: estimation
62F10 Point estimation
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