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On the Asymptotic Behaviour of Posterior Distributions

后验分布的渐近行为

Summary Let a random sample of size n be taken from a distribution having a density depending on a real parameter θ, and let θ have an absolutely continuous prior distribution with density π(θ). We give a rigorous proof that, under suitable regularity conditions, the posterior distribution of θ will, when n tends to infinity, be asymptotically normal with mean equal to the maximum-likelihood estimator and variance equal to the reciprocal of the second derivative of the…

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A Note on the Asymptotic Distribution of Sample Quantiles

样本分位数渐近分布的一则说明

Summary This paper gives a rigorous proof, under conditions believed to be minimal, of the asymptotic normality of a finite set of quantiles of a random sample from an absolutely continuous distribution. The proof is substantially simpler than those that have previously been published.

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A Note on the Asymptotic Efficiency of an Asymptotically Normal Estimator Sequence

关于渐近正态估计量序列渐近效率的一则说明

SUMMARY This paper gives a rigorous yet quite elementary proof that under fairly general conditions, the asymptotic efficiency of an asymptotically normal estimator sequence does not exceed unity. Both estimation of a single parameter and simultaneous estimation of several parameters are considered.

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Large-sample estimation of parameters for autoregressive processes with moving-average residuals

含移动平均残差的自回归过程参数的大样本估计

A. M. WALKER; Large-sample estimation of parameters for autoregressive processes with moving-average residuals, Biometrika, Volume 49, Issue 1-2, 1 January 1962

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On Durbin's formula for the limiting generalized variance of a sample of consecutive observations from a moving-average process

论移动平均过程连续观测样本极限广义方差的 Durbin 公式

A. M. WALKER; On Durbin's formula for the limiting generalized variance of a sample of consecutive observations from a moving-average process, Biometrika, Volum

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A GOODNESS OF FIT TEST FOR SPECTRAL DISTRIBUTION FUNCTIONS OF STATIONARY TIME SERIES WITH NORMAL RESIDUALS

具有正态残差的平稳时间序列谱分布函数的拟合优度检验

A. M. WALKER; A GOODNESS OF FIT TEST FOR SPECTRAL DISTRIBUTION FUNCTIONS OF STATIONARY TIME SERIES WITH NORMAL RESIDUALS, Biometrika, Volume 43, Issue 3-4, 1 De

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Some Properties of the Asymptotic Power Functions of Goodness-of-Fit Tests for Linear Autoregressive Schemes

线性自回归模型拟合优度检验的渐近功效函数性质

Summary Quenouille (1947), and Bartlett and Diananda (1950), have given large sample goodness-of-fit tests of the hypothesis that a time series can be represented by a linear autoregressive scheme with independent residuals. Asymptotic power functions of these tests are derived for alternative hypotheses specified by linear autoregressive schemes of higher order with independent residuals, and of the same or higher order with residuals among which there exists dependence of…

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