arXiv subjects

Jixuan Liu

Publications and source records attributed to Jixuan Liu.

6 recordsLinked to original sources

arXiv2026

High-Dimensional Change Point Analysis for Temporally Dependent Data

This paper develops adaptive procedures for detecting and locating mean changes in high-dimensional time series. Quadratic CUSUM statistics target dense changes, whereas coordinatewise maximum statistics target sparse changes. Two weighting schemes are considered to accommodate both interior and boundary changes. Under general non-Gaussian vector dependence, we establish the limiting distributions, validate the required centering and scaling estimators, and prove asymptotic independence between matched quadratic and maximum statistics. These results justify Cauchy combination tests. We further establish single-change localization and consistent multiple-change recovery using wild binary segmentation. Numerical results illustrate the effectiveness of the proposed methods.

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arXiv2025

Adaptive Change Point Inference for High Dimensional Time Series with Temporal Dependence

This paper investigates change point inference in high-dimensional time series. We begin by introducing a max-$L_2$-norm based test procedure, which demonstrates strong performance under dense alternatives. We then establish the asymptotic independence between our proposed statistic and the two max-$L_\infty$-based statistics introduced by Wang and Feng (2023). Building on this result, we develop an adaptive inference approach by applying the Cauchy combination method to integrate these tests. This combined procedure exhibits robust performance across varying levels of sparsity. Extensive simulation studies and real data analysis further confirm the superior effectiveness of our proposed methods in the high-dimensional setting.

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arXiv2025

Tensor Elliptical Graphic Model

We address the problem of robust estimation of sparse high dimensional tensor elliptical graphical model. Most of the research focus on tensor graphical model under normality. To extend the tensor graphical model to more heavy-tailed scenarios, motivated by the fact that up to a constant, the spatial-sign covariance matrix can approximate the true covariance matrix when the dimension turns to infinity under tensor elliptical distribution, we proposed a spatial-sign-based estimator to robustly estimate tensor elliptical graphical model, the rate of which matches the existing rate under normality for a wider family of distribution, i.e. elliptical distribution. We also conducted extensive simulations and real data applications to illustrate the practical utility of the proposed methods, especially under heavy-tailed distribution.

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arXiv2025

Spatial-Sign based High dimensional Change Point Inference

High-dimensional changepoint inference, adaptable to diverse alternative scenarios, has attracted significant attention in recent years. In this paper, we propose an adaptive and robust approach to changepoint testing. Specifically, by generalizing the classical mean-based cumulative sum (CUSUM) statistic, we construct CUSUM statistics based on spatial medians and spatial signs. We introduce test statistics that consider the maximum and summation of the CUSUM statistics across different dimensions, respectively, and take the maximum across all potential changepoint locations. The asymptotic distributions of test statistics under the null hypothesis are derived. Furthermore, the test statistics exhibit asymptotic independence under mild conditions. Building on these results, we propose an adaptive testing procedure that combines the max-$L_\infty$-type and max-$L_2$-type statistics to achieve high power under both sparse and dense alternatives. Through numerical experiments and theoretical analysis, the proposed method demonstrates strong performance and exhibits robustness across a wide range of signal sparsity levels and heavy-tailed distributions.

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arXiv2024

Spatial-Sign based Maxsum Test for High Dimensional Location Parameters

In this study, we explore a robust testing procedure for the high-dimensional location parameters testing problem. Initially, we introduce a spatial-sign based max-type test statistic, which exhibits excellent performance for sparse alternatives. Subsequently, we demonstrate the asymptotic independence between this max-type test statistic and the spatial-sign based sum-type test statistic (Feng and Sun, 2016). Building on this, we propose a spatial-sign based max-sum type testing procedure, which shows remarkable performance under varying signal sparsity. Our simulation studies underscore the superior performance of the procedures we propose.

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arXiv2024

TUNE: Algorithm-Agnostic Inference after Changepoint Detection

In multiple changepoint analysis, assessing the uncertainty of detected changepoints is crucial for enhancing detection reliability -- a topic that has garnered significant attention. Despite advancements through selective p-values, current methodologies often rely on stringent assumptions tied to specific changepoint models and detection algorithms, potentially compromising the accuracy of post-detection statistical inference. We introduce TUNE (Thresholding Universally and Nullifying change Effect), a novel algorithm-agnostic approach that uniformly controls error probabilities across detected changepoints. TUNE sets a universal threshold for multiple test statistics, applicable across a wide range of algorithms, and directly controls the family-wise error rate without the need for selective p-values. Through extensive theoretical and numerical analyses, TUNE demonstrates versatility, robustness, and competitive power, offering a viable and reliable alternative for model-agnostic post-detection inference.

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