Asymptotically optimal parameter estimation under communication constraints
Asymptotically optimal parameter estimation under communication constraints
复制标题
通信约束下的渐近最优参数估计
DOI：
10.1214/12-aos1035
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发表时间：
2011
影响因子：
4.5
通讯作者：
Georgios Fellouris
中科院分区：
文献类型：
--
作者：
Georgios Fellouris
考虑了一个参数估计问题，其中分散的传感器向统计学家传递有关其观测值的部分信息。传感器观察连续半鞅的路径，其漂移相对于一个公共参数是线性的。提出了一种新的估计方案，每个传感器在其局部滤波停止时间只发送1位信息。所提出的估计量被证明是一致的，并且对于一大类过程是渐近最优的，因为它的渐近分布与具有完全访问传感器观测值的最优估计量的精确分布相同。这些性质是在传感器和统计学家之间的渐近低通信速率下建立的。因此，尽管渐近有效，但所提出的估计器需要最小的传输活动，这在许多应用中是理想的特性。最后，研究了传感器底层过程为独立布朗运动时的离散采样情况。
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear with respect to a common parameter. A novel estimating scheme is suggested, according to which each sensor transmits only one-bit messages at stopping times of its local filtration. The proposed estimator is shown to be consistent and, for a large class of processes, asymptotically optimal, in the sense that its asymptotic distribution is the same as the exact distribution of the optimal estimator that has full access to the sensor observations. These properties are established under an asymptotically low rate of communication between the sensors and the statistician. Thus, despite being asymptotically efficient, the proposed estimator requires minimal transmission activity, which is a desirable property in many applications. Finally, the case of discrete sampling at the sensors is studied when their underlying processes are independent Brownian motions.