Statistical Inference for Student Diffusion Process
Statistical Inference for Student Diffusion Process
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DOI：
10.1080/07362994.2010.515476
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发表时间：
2010-01-01
影响因子：
1.3
通讯作者：
Suvak, N.
中科院分区：
文献类型：
--
作者：
Leonenko, N. N.;Suvak, N.
我们考虑具有对称缩放学生不变分布的遍历扩散的参数估计问题，其中过渡密度的谱表示是根据有限数量的多项式本征函数（劳斯-罗曼诺夫斯基多项式）和观察到的扩散的负无穷小生成器的绝对连续谱给出的。我们证明了所提出的估计量的一致性和渐近正态性，并基于学生扩散的斯坦因方程，考虑学生分布假设的统计检验。
We consider the problem of parameter estimation for an ergodic diffusion with the symmetric scaled Student invariant distribution, where the spectral representation of the transition density is given in terms of the finite number of polynomial eigenfunctions (Routh-Romanovski polynomials) and absolutely continuous spectrum of the negative infinitesimal generator of observed diffusion. We prove the consistency and asymptotic normality of the proposed estimators and, based on the Stein equation for Student diffusion, consider the statistical test for the Student distributional assumptions.