论文检索

对《状态空间模型中的有效似然估计》相关问题评论的回复AI 解读

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root…

具有先后约束的一类序贯控制问题的最优策略AI 解读

Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each phase, one can pursue the projects in any order. When pursuing the project with one unit of resource, the project state changes according to a Markov chain. The probability distribution of the Markov chain is known up to an unknown…

状态空间模型中的有效似然估计AI 解读

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root…

隐马尔可夫模型中最优变点检测的渐近运行特性AI 解读

Let ξ0,ξ1,…,ξω−1 be observations from the hidden Markov model with probability distribution Pθ0, and let ξω,ξω+1,… be observations from the hidden Markov model with probability distribution Pθ1. The parameters θ0 and θ1 are given, while the change point ω is unknown. The problem is to raise an alarm as soon as possible after the distribution changes from Pθ0 to Pθ1, but to avoid false alarms. Specifically, we seek a stopping rule N which allows us to observe the ξ's…

隐 Markov 模型中的 SPRT 与 CUSUMAI 解读

In this paper, we study the problems of sequential probability ratio tests for parameterized hidden Markov models. We investigate in some detail the performance of the tests and derive corrected Brownian approximations for error probabilities and expected sample sizes. Asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden Markov chain data is established. Next, we consider the cumulative sum (CUSUM) procedure for change…

Motivated by an application in computerized adaptive tests, we consider the following sequential design problem.There are $J$ jobs to be processed according to a predetermined order. A single machine is available to process these $J$ jobs. Each job under processing evolves stochastically as a Markov chain and earns rewards as it is processed, not otherwise. The Markov chain has transition probabilities parameterized by an unknown parameter $\theta$. The objective is to…