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英文文献：Efficient Estimation for Diffusions Sampled at High Frequency Over a Fixed Time Interval-在固定时间间隔内高频采样的扩散的有效估计
英文文献作者：Nina Munkholt Jakobsen,Michael S?rensen
英文文献摘要：
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find easily verified conditions on approximate martingale estimating functions under which estimators are consistent, rate optimal, and efficient under high frequency (in-fill) asymptotics. The asymptotic distributions of the estimators are shown to be normal variance-mixtures, where the mixing distribution generally depends on the full sample path of the diffusion process over the observation time interval. Utilising the concept of stable convergence, we also obtain the more easily applicable result that for a suitable data dependent normalisation, the estimators converge in distribution to a standard normal distribution. The theory is illustrated by a small simulation study comparing an efficient and a non-efficient estimating function.
研究了固定时间区间内高频观测扩散过程的参数估计。该过程求解扩散系数为未知参数的随机微分方程。摘要在高频(填充)渐近下，我们得到了一些易于验证的近似鞅估计函数的条件，在这些条件下，估计量是一致的、速率最优的和有效的。估计量的渐近分布是正态的方差混合分布，其中混合分布一般依赖于扩散过程在观测时间区间内的全样本路径。利用稳定收敛的概念，我们还得到了一个更容易适用的结果，即对于一个合适的数据相关正态化，估计量在分布上收敛到一个标准正态分布。通过一个小型的仿真研究，比较了一个有效的估计函数和一个无效的估计函数，说明了该理论。
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