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利用广义距离相关检验独立性AI 解读

We study the fundamental statistical inference concerning the testing of independence between two random vectors. Existing asymptotic theories for test statistics based on distance covariance can only apply to either low-dimensional or high-dimensional settings and require stringent distributional assumptions. In this work we develop a new unified distributional theory of the sample generalized distance covariance that works for random vectors of arbitrary dimensions under…

高维局部平稳过程的协方差与谱密度估计收敛性AI 解读

Covariances and spectral density functions play a fundamental role in the theory of time series. There is a well-developed asymptotic theory for their estimates for low-dimensional stationary processes. For high-dimensional nonstationary processes, however, many important problems on their asymptotic behaviors are still unanswered. This paper presents a systematic asymptotic theory for the estimates of time-varying second-order statistics for a general class of…

Pearson 卡方统计量：近似理论及其扩展AI 解读

Summary We establish an approximation theory for Pearson’s chi-squared statistics in situations where the number of cells is large, by using a high-dimensional central limit theorem for quadratic forms of random vectors. Our high-dimensional central limit theorem is proved under Lyapunov-type conditions that involve a delicate interplay between the dimension, the sample size, and the moment conditions. We propose a modified chi-squared statistic and introduce an adjusted…

非平稳 AR(1) 模型中的结构变化AI 解读

This article revisits the asymptotic inference for nonstationary AR(1) models of Phillips and Magdalinos (2007a) by incorporating a structural change in the AR parameter at an unknown time k 0 . Consider the model ${y_t} = {\beta _1}{y_{t - 1}}I\{ t \le {k_0}\} + {\beta _2}{y_{t - 1}}I\{ t > {k_0}\} + {\varepsilon _t},t = 1,2, \ldots ,T$ , where I {·} denotes the indicator function, one of ${\beta _1}$ and ${\beta _2}$ depends on the sample size T , and the other is equal to…

高维时间序列的高斯近似AI 解读

We consider the problem of approximating sums of high dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$, the dimension $p$, the moment condition and the dependence of the underlying processes. We also consider an estimator for long-run covariance matrices and study its convergence properties. Our results allow constructing simultaneous…