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拟似然与 EM 算法的推广AI 解读

SUMMARY This paper is concerned with situations in which there are missing or otherwise incomplete data and the full likelihood may not be available. Extensions of the EM algorithm are developed to deal with estimation via general estimating functions and in particular the quasi-score. The E-step is replaced by projecting the quasi-score and the M-step requires the solution of an estimating equation. The standard EM algorithm can be obtained as a particular case if the…

约束拟似然估计AI 解读

For maximum likelihood or least squares parameter estimation subject to a constrained parameter, the standard approach is to use the method of Lagrange multipliers. In this paper it is shown that the same formal procedure applies very generally for constrained quasi-likelihood estimation even though there is ordinarily no objective function to maximize or minimize. This allows for optimal estimation in a wide range of problems where maximum likelihood cannot be used, such as…

受约束的拟似然估计AI 解读

For maximum likelihood or least squares parameter estimation subject to a constrained parameter, the standard approach is to use the method of Lagrange multipliers. In this paper it is shown that the same formal procedure applies very generally for constrained quasi-likelihood estimation even though there is ordinarily no objective function to maximize or minimize. This allows for optimal estimation in a wide range of problems where maximum likelihood cannot be used, such as…

随机过程参数的最优渐近置信区间AI 解读

This paper is concerned with the size of confidence intervals for parameters of stochastic processes based on limit laws with two competing normalizations, one producing asymptotic normality and the other asymptotic mixed normality. It is shown that, in a certain sense, the interval based on asymptotic normality is preferable on average. Applications to estimation of parameters in nonergodic stochastic processes and to estimation of steady-state parameters in a simulation…

一类允许长程依赖的随机场模型AI 解读

In this note it is shown how a convenient class of random field models with rational spectral densities can be augmented to incorporate the possibility of long range dependence.

允许长程依赖的一类随机场模型AI 解读

In this note it is shown how a convenient class of random field models with rational spectral densities can be augmented to incorporate the possibility of long range dependence.

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随机过程参数后验分布的渐近正态性AI 解读

Summary Asymptotic normality of the posterior distribution of a parameter in a stochastic process is shown to hold under conditions which do little more than ensure consistency of a maximum likelihood estimator. Much more stringent conditions are required to ensure asymptotic normality of the MLE. This contrast, which has implications of considerable significance, does not emerge in the classical context of independent and identically distributed observations.

分枝过程参数估计效率的几点讨论AI 解读

This paper is concerned with efficiency in the estimation of the mean θ of the offspring distribution of a supercritical Galton-Watson branching process on the basis of a sample of n consecutive generation sizes. First, a direct comparison is made between the maximum likelihood estimator and the simple ratio of generation sizes estimator. Next, a new definition of asymptotic efficiency of an estimator is given, generalizing that of Rao (1973). It is shown that, for offspring…

经典更新理论自然推广的渐近结果AI 解读

Summary A generalization of the classical renewal theory for non-negative summands is suggested which involves the maxima of the partial sums instead of the partial sums themselves. It is shown that the generalization is a natural one and that most of the classical properties are preserved. In addition, methods are developed for obtaining asymptotic expansions for the moments of the random variable whose expectation is the new renewal function.