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使用无偏似然估计时的 MCMC 高效实现AI 解读

When an unbiased estimator of the likelihood is used within a Metropolis–Hastings chain, it is necessary to trade off the number of Monte Carlo samples used to construct this estimator against the asymptotic variances of the averages computed under this chain. Using many Monte Carlo samples will typically result in Metropolis–Hastings averages with lower asymptotic variances than the corresponding averages that use fewer samples; however, the computing time required to…

混合谱时间序列的半参数贝叶斯推断AI 解读

Summary A Bayesian analysis is presented of a time series which is the sum of a stationary component with a smooth spectral density and a deterministic component consisting of a linear combination of a trend and periodic terms. The periodic terms may have known or unknown frequencies. The advantage of our approach is that different features of the data—such as the regression parameters, the spectral density, unknown frequencies and missing observations—are combined in a…

状态空间模型的吉布斯抽样AI 解读

We show how to use the Gibbs sampler to carry out Bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time. Our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors. The states are generated efficiently using the Kalman filter. We illustrate our…

存在缺失或聚合数据时向量ARMA过程的精确似然AI 解读

This note points out that by using the Kalman filter with nonconstant coefficients, we can compute the exact likelihood of an autoregressive-moving average process observed with noise, when some of our observations are either missing or aggregated.

最小参数子集维数的一致估计AI 解读

For a general paramnetric model we consider the problem of consistently estimating that permissible subset of the parameter space that contains the true parameter point and has smallest dimension. The subset selection is done by means of a model selection criterion of

缺失或聚合数据下向量 ARMA 过程的精确似然AI 解读

This note points out that by using the Kalman filter with nonconstant coefficients, we can compute the exact likelihood of an autoregressive-moving average process observed with noise, when some of our observations are either missing or aggregated.

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向量线性时间序列模型的渐近估计与假设检验结果AI 解读

For a general vector linear time series model we prove the strong consistency and asymptotic normality of parameter estimates obtained by maximizing a particular time domain approximation to a Gaussian likelihood, although we do not assume that the observations are necessarily normally distributed. To solve the normal equations we set up a constrained Gauss-Newton iteration and obtain the properties of the iterates when the sample size is large. In particular we show that…

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关于自回归移动平均过程的 Akaike 与 Hannan 估计程序AI 解读

We demonstrate that the estimator proposed by Akaike (1973) is exactly the first step of a Gauss-Newton algorithm applied to the exponent of a Gaussian likelihood and show its relationship to the estimator proposed by Hannan (1969).