Divide and Conquer: Recursive Likelihood Function Integration for Hidden Markov Models with Continuous Latent Variables
提出一种完全确定性的递归积分方案，用于在计算似然函数时积分掉未观测状态，避免了蒙特卡洛模拟噪声，并证明了数值误差界和收敛速度。
A common problem in the estimation of structural economic decision models is that only a subset of the information available to the decision maker is present in the data. Therefore, an econometrician estimating the model needs to “integrate out” these unobserved states. Until recently, all approaches to this problem involved Monte Carlo techniques, making maximum likelihood estimation difficult due to the presence of simulation noise. In “Divide and Conquer: Recursive Likelihood Function Integration for Hidden Markov Models with Continuous Latent Variables,” G. Reich develops an efficient and fully deterministic integration scheme to recursively integrate out unobserved states when computing the likelihood function. Moreover, he proves numerical error bounds and convergence rates that suggest that the method is highly efficient under appropriate smoothness conditions, which is confirmed in several examples. In particular, he estimates an extension of the famous bus engine replacement model of Rust (1987) allowing for serially correlated errors.