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一般矩变点的最优检测：均值与协方差变点同时检测及推广AI 解读

We study multiple change-point detection in multivariate time series whose distributions change in a piecewise constant manner. Distributional changes can manifest across different moment orders, from shifts in the mean and covariance to changes in higher-order moments. Higher-order moments capture increasingly rich distributional features but become difficult to estimate in high dimensions. Our tensor representation unifies moments of different orders within a common linear…

高维及可能非平稳时间序列的尾部稳健自协方差矩阵估计AI 解读

In this paper, we study the autocovariance matrix estimation and inference problems under heavy-tailedness, high-dimensionality, general nonlinear temporal dependence, and potentially nonstationarity of time series. We consider two types of tail-robust autocovariance matrix estimation methods: the element-wise Huber's $M$-estimator and a computationally more efficient element-wise truncated estimator. Both estimators are designed to achieve sharp error bounds in matrix…

多元非齐次泊松过程时间序列的在线变点检测AI 解读

We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains underexplored in the machine learning and statistics literature. We propose a method that uses low-rank matrices to represent the multivariate Poisson intensity functions, resulting in an adaptive nonparametric detection procedure. Our…

函数型回归时间序列变点的估计与推断AI 解读

In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is computationally efficient as well as achieving consistency in multiple change point detection. This algorithm utilizes the predictive power of piece-wise constant functional linear regression models in the reproducing kernel Hilbert space…

时间依赖下高维回归模型的变点推断AI 解读

This paper concerns about the limiting distributions of change point estimators, in a high-dimensional linear regression time series context, where a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed at every time point $t \in \{1, \ldots, n\}$. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in $\ell_2$-norm. We provide limiting distributions of the change point estimators in the…

混合条件下多变量非参数模型的变化点检测与推断AI 解读

This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be piecewise constant with densities in a Hölder class. The change points, or times at which the distribution changes, are unknown. We derive the limiting distributions of the change point estimators when the minimal jump size vanishes or remains…