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半参数模型中光滑泛函的 Bernstein–von Mises 定理AI 解读

A Bernstein–von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems in i.i.d. and non-i.i.d. situations. In particular, new tools are developed to handle semiparametric bias, in particular for nonlinear functionals and in cases where regularity is possibly low. Examples include the squared $L^{2}$-norm in Gaussian white noise, nonlinear functionals in density estimation, as well as functionals in…

长记忆或中间记忆高斯过程谱密度的贝叶斯非参数估计AI 解读

A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density $f(\lambda)$ can be written as $f(\lambda)=|\lambda|^{-2d}g(|\lambda|)$, where $0<d<1/2$ (resp., $-1/2<d<0$), and $g$ is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation of the spectral density of such processes. We prove posterior consistency for both $d$ and $g$, under appropriate conditions on the prior…

平稳高斯过程记忆参数极大似然估计的渐近理论AI 解读

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045–1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility.

平稳高斯强相依过程参数最大似然估计的有效渐近展开AI 解读

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA-type models, including fractional Gaussian noise. The method of proof consists of three main ingredients: (i) verification of a suitably modified version of Durbin's general conditions for the validity of the Edgeworth expansion to the joint density of the log-likelihood…

长程依赖下样本自相关函数的有效 Edgeworth 展开AI 解读

We prove in this paper the validity of an Edgeworth expansion to the joint distribution of the sample autocorrelations of a stationary Gaussian long memory process. The method of proof relies on a verification of the suitably modified conditions for the validity of a multivariate Edgeworth expansion of Durbin (1980, Biometrika 67, 311–333). A simulation study proves the expansion to be useful and accurate.

ARFIMA 模型中基于似然的小样本推断AI 解读

The autoregressive fractionally integrated moving average (ARFIMA) model has become a popular approach for analyzing time series that exhibit long-range dependence. For the Gaussian case, there have been substantial advances in the area of likelihood-based inference, including development of the asymptotic properties of the maximum likelihood estimates and formulation of procedures for their computation. Small-sample inference, however, has not to date been studied. Here we…