基于UD分解的成对与MIMO类卡尔曼滤波在计量经济学模型结构估计中的应用
UD-based pairwise and MIMO Kalman-like filtering for estimation of econometric model structures
AI总结：
本文针对计量经济学模型，研究了LTI MIMO系统和PMM，设计了基于解析梯度和$UDU^\ op$分解的鲁棒自适应类卡尔曼滤波方法，实现了高效准确的状态与参数同时估计。
摘要：
计量经济学现代研究方向之一是将各种结构计量经济学模型转化为状态空间形式，从而通过卡尔曼滤波方案实现高效的未知动态系统状态和参数估计。这一趋势催生了先进的状态空间模型结构，要求根据应用需求设计创新的估计技术。本文研究了线性时不变多输入多输出系统（LTI MIMO）以及成对马尔可夫模型（PMM）及其相关的成对卡尔曼滤波器（PKF）。具体而言，我们设计了基于梯度的鲁棒自适应类卡尔曼滤波方法，用于上述模型结构中的状态和参数同时估计。由于在计算中利用了解析计算的梯度而非数值近似，我们的方法快速且准确。此外，这些方法采用了数值鲁棒的基于$UDU^\ op$分解的卡尔曼滤波实现，在实践中具有可靠性。我们的新技术在数值算例上进行了检验，并用于处理计量经济学中的一个随机模型。
英文摘要：
One of the modern research lines in econometrics studies focuses on translating a wide variety of structural econometric models into their state-space form, which allows for efficient unknown dynamic system state and parameter estimations by the Kalman filtering scheme. The mentioned trend yields advanced state-space model structures, which demand innovative estimation techniques driven by application requirements to be devised. This paper explores both the linear time-invariant multiple-input, multiple-output system (LTI MIMO) and the pairwise Markov model (PMM) with the related pairwise Kalman filter (PKF). In particular, we design robust gradient-based adaptive Kalman-like filtering methods for the simultaneous state and parameter estimation in the outlined model structures. Our methods are fast and accurate because their analytically computed gradient is utilized in the calculation instead of its numerical approximation. Also, these employ the numerically robust $UDU^\top$-factorization-based Kalman filter implementation, which is reliable in practice. Our novel techniques are examined on numerical examples and used for treating one stochastic model in econometrics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
