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关于程德福《状态空间模型中的有效似然估计》一文的若干问题
On some problems in the article "Efficient Likelihood Estimation in State Space Models" by Cheng-Der Fuh [Ann. Statist. 34 (2006) 2026--2068] [arXiv:math/0611376]
状态空间模型中最大似然估计量的渐近正态性
State space models is a very general class of time series models capable of modelling dependent observations in a natural and interpretable way. Inference in such models has been studied by Bickel, Ritov and Rydén, who consider hidden Markov models, which are special kinds of state space models, and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions. In this paper we generalize the results of Bickel, Ritov and Rydén to state…
一致鞍点近似与对数凹密度
SUMMARY For a one-dimensional variable with a log-concave density it is shown that the saddlepoint approximations to the density and the distribution function of the mean are uniformly valid. A double-saddlepoint approximation to a conditional distribution function is introduced, which is uniformly valid for a two-dimensional log-concave density. The results are illustrated with the log-normal distribution and the gamma distribution.
“Box 类”似然比准则的大偏差型近似
For a large class of tests related to the multivariate normal distribution a number of approximations to the distribution of the log-likelihood ratio statistic are discussed. Some of the approximations require the use of a small personal computer for their calculation, but this pays off in terms of giving very accurate approximations. Actually, one of the approximations, based on the use of a conjugate distribution, works well for all sample sizes and all significance levels.
离散情形中的“改进似然比统计量”真的改进了吗？
On the basis of some numerical studies we argue that Bartlett adjustment of the likelihood ratio statistic for discrete data does not in general yield an improvement in the asymptotic error rate of the chi-squared approximation. Also we argue that the small-sample effect of the Bartlett adjustment is unclear and that it is in no way comparable with the improvement obtained for continuous data.