Efficiency and Robustness of Fully Adaptive Simulated Maximum Likelihood Method
- Authors
- 오만숙; 김대경
- Issue Date
- May-2009
- Publisher
- 한국통계학회
- Keywords
- Monte Carlo; importance sampling; marginal likelihood; missing
- Citation
- Communications for Statistical Applications and Methods, v.16, no.3, pp.479 - 485
- Indexed
- KCI
- Journal Title
- Communications for Statistical Applications and Methods
- Volume
- 16
- Number
- 3
- Start Page
- 479
- End Page
- 485
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/41662
- ISSN
- 2287-7843
- Abstract
- When a part of data is unobserved the marginal likelihood of parameters given the observed data often involves analytically intractable high dimensional integral and hence it is hard to find the maximum likelihood estimate of the parameters. Simulated maximum likelihood(SML) method which estimates the marginal likelihood via Monte Carlo importance sampling and optimize the estimated marginal likelihood has been used in many applications. A key issue in SML is to find a good proposal density from which
Monte Carlo samples are generated. The optimal proposal density is the conditional density of the unobserved data given the parameters and the observed data, and attempts have been given to find a good approximation to the optimal proposal density. Algorithms which adaptively improve the proposal density have been widely used due to its simplicity and efficiency. In this paper, we describe a fully adaptive algorithm which has been used by some practitioners but has not been well recognized in statistical
literature, and evaluate its estimation performance and robustness
via a simulation study. The simulation study shows a great
improvement in the order of magnitudes in the mean squared error,
compared to non-adaptive or partially adaptive SML methods. Also,
it is shown that the fully adaptive SML is robust in a sense that
it is insensitive to the starting points in the optimization
routine.
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