Quasi likelihood analysis of volatility and nondegeneracy of statistical random field
Quasi likelihood analysis of volatility and nondegeneracy of statistical random field
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DOI：
10.1016/j.spa.2013.04.008
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发表时间：
2013-07
影响因子：
1.4
通讯作者：
Masayuki Uchida;N. Yoshida
中科院分区：
文献类型：
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作者：
Masayuki Uchida;N. Yoshida
本文构造了有限时间区间上高频采样下扩散过程的拟似然分析。为此，我们证明了拟似然随机场的一个多项式型大偏差不等式。然后证明关键指标χ0的非退化性就变得至关重要。根据抽样设置的性质，χ 0是随机的。这使得很难应用一个朴素的充分条件，并需要一个新的机制。为了建立拟似然分析，需要对χ0的非退化性进行定量估计.与统计随机场相关联的某个张量丛的非退化局部截面的存在解决了这个问题。
We construct a quasi likelihood analysis for diffusions under the high-frequency sampling over a finite time interval. For this, we prove a polynomial type large deviation inequality for the quasi likelihood random field. Then it becomes crucial to prove nondegeneracy of a key index χ0. By nature of the sampling setting, χ0is random. This makes it difficult to apply a naïve sufficient condition, and requires a new machinery. In order to establish a quasi likelihood analysis, we need quantitative estimate of the nondegeneracy of χ0. The existence of a nondegenerate local section of a certain tensor bundle associated with the statistical random field solves this problem.