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高维长期方差与精度矩阵的局部 Whittle 估计AI 解读

This work develops nonasymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including long-range dependence. The estimation involves shrinkage techniques, which are thresholding and penalizing versions of the classical multivariate local Whittle estimator. The results ensure consistent estimation in a double asymptotic regime…

潜在高斯计数时间序列AI 解读

This article develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very flexible correlation features that can have any prespecified marginal distribution, including the classical Poisson, generalized Poisson, negative binomial, and binomial structures. Gaussian pseudo-likelihood and implied Yule–Walker…

计数时间序列：方法综述AI 解读

A growing interest in non-Gaussian time series, particularly in series comprised of nonnegative integers (counts), is taking place in today’s statistics literature. Count series naturally arise in fields, such as agriculture, economics, epidemiology, finance, geology, meteorology, and sports. Unlike stationary Gaussian series where autoregressive moving-averages are the primary modeling vehicle, no single class of models dominates the count landscape. As such, the literature…

多元变系数模型的局部与全局秩检验AI 解读

In a multivariate varying-coefficient model, the response vectors Y are regressed on known functions v(X) of some explanatory variables X and the coefficients in an unknown regression matrix θ(Z) depend on another set of explanatory variables Z. We provide statistical tests, called local and global rank tests, which allow one to estimate the rank of an unknown regression coefficient matrix θ(Z) locally at a fixed level of the variable Z or globally as the maximum rank over…

对称矩阵的秩估计：不定矩阵估计量情形AI 解读

In this paper we consider estimating the rank of an unknown symmetric matrix based on a symmetric, asymptotically normal estimator of the matrix. The related positive definite limit covariance matrix is assumed to be estimated consistently and to have either a Kronecker product or an arbitrary structure. These assumptions are standard although they exclude the case when the matrix estimator is positive or negative semidefinite. We adapt and reexamine here some available rank…