论文标题
高斯的准信息标准，用于lévy驱动的SDE
Gaussian quasi-information criteria for ergodic Lévy driven SDE
论文作者
论文摘要
我们考虑了在高频上观察到的半参数lévy驱动模型的参数系数的相对模型比较。我们的渐近学基于Euler-Approximation类型的完全显式两阶段的高斯准易头函数（GQLF）。对于量表和漂移系数的选择，我们建议通过逐步推理过程提出显式高斯准AIC（GQAIC）和高斯准BIC（GQBIC）统计。特别是，我们表明，在扩散情况下不会出现关节GQLF的混合速率结构，从而在选择量表系数的选择中会导致正则化项的非标准形式，从而定量阐明了估计精度和采样频率之间的关系。进行数值实验以说明我们的理论发现。
We consider relative model comparison for the parametric coefficients of a semiparametric ergodic Lévy driven model observed at high-frequency. Our asymptotics is based on the fully explicit two-stage Gaussian quasi-likelihood function (GQLF) of the Euler-approximation type. For selections of the scale and drift coefficients, we propose explicit Gaussian quasi-AIC (GQAIC) and Gaussian quasi-BIC (GQBIC) statistics through the stepwise inference procedure. In particular, we show that the mixed-rates structure of the joint GQLF, which does not emerge for the case of diffusions, gives rise to the non-standard forms of the regularization terms in the selection of the scale coefficient, quantitatively clarifying the relation between estimation precision and sampling frequency. Numerical experiments are given to illustrate our theoretical findings.
