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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…

基于局部自适应回归样条的时空模型AI 解读

This paper focuses on the estimation of a non-parametric regression function in the presence of data with spatio-temporal dependencies. In such a context, we study Locally Adaptive Regression Splines, a nonparametric estimator introduced by Mammen and Van De Geer (1997) and Rudin et al. (1992). To the best of our knowledge, this estimator has not previously been examined in a similar context. For univariate settings, the signals we consider are assumed to have a kth weak…

时间依赖下高维线性模型的最优变点检验AI 解读

In this paper, we study change-point testing for high-dimensional linear models, an important problem that has not been well explored in the literature. Specifically, we propose a quadratic-form cumulative sum (CUSUM) statistic to test the stability of regression coefficients in high-dimensional linear models. The test controls type-I error at any desired level and is robust to temporally dependent observations. We establish its asymptotic distribution under the null…

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…

分治动态规划：高维变点检测的近线性时间方法AI 解读

We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy algorithms that are applicable to a broad variety of high-dimensional statistical models and can enjoy almost linear computational complexity. We investigate the performance of DCDP in three commonly studied change point settings in high…

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…

序贯成对比较数据中突变的检测AI 解读

The Bradley-Terry-Luce (BTL) model is a classic and very popular statistical approach for eliciting a global ranking among a collection of items using pairwise comparison data. In applications in which the comparison outcomes are observed as a time series, it is often the case that data are non-stationary, in the sense that the true underlying ranking changes over time. In this paper we are concerned with localizing the change points in a high-dimensional BTL model with…