arXiv subjects

Long Feng

Publications and source records attributed to Long Feng.

At least 19 recordsLinked to original sources

arXiv2026

Analytically Calibrated Upper L-Statistics for High-Dimensional Mean Change-Point Testing

This paper develops upper L-statistic methods for testing and localizing a high-dimensional mean change. At each candidate split, the proposed statistics rank the squared studentized CUSUM values across coordinates and aggregate either a fixed number or a fixed proportion of the largest entries. This construction connects max-type and sum-type procedures and provides sensitivity to a wide range of sparsity regimes. We establish asymptotic null distributions under an independent-component representation allowing weak cross-sectional dependence. The limiting laws are Poisson tangent processes for fixed ranks and Gaussian-process or Gumbel laws for proportional ranks. To improve finite-sample performance, we develop analytic calibrations for marginal variance estimation, cross-sectional dependence, extreme clustering, and skewness, and establish their first-order validity. We combine calibrated p-values from a matched pair of fixed- and proportional-order statistics using the Cauchy combination rule to adapt to unknown sparsity. For localization, the estimated change point is selected from the component scan with the smallest p-value. Simulation studies demonstrate generally satisfactory size calibration, competitive detection power, and effective localization across different sparsity levels. An application to semiconductor manufacturing data further illustrates the practical utility of the proposed methods.

stat.ME↗

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.

stat.ME↗

arXiv2026

Boot-AVT: Asymptotically Anytime-Valid Testing with Degenerate U-Statistics via Bootstrap

Many nonparametric tests are based on $U$-statistics that are degenerate under the null hypothesis. We develop Boot-AVT, a bootstrap procedure for asymptotically anytime-valid testing with these statistics. Using Brownian scaling and time inversion for the limiting Gaussian chaos process, we show that logarithmically penalized maxima over observed and future sample sizes have a common limiting null distribution. A quadratic multiplier bootstrap estimates the corresponding critical values. We also develop Boot-AVT-Multi for joint testing with multiple kernels. For both procedures, we establish uniform consistency of the bootstrap critical values, explicit bounds on size distortion, and asymptotic size $α$ over an unbounded monitoring horizon as the monitoring start tends to infinity. Under fixed alternatives, we derive finite-horizon power bounds and establish power one with finite expected stopping times. Simulation studies evaluate finite-sample size and power in goodness-of-fit, two-sample and independence testing, and real-data analyses compare stopping times.

math.ST↗

arXiv2026

Cauchy-Combined Hettmansperger-Randles Location Tests in High Dimensions

High-dimensional mean testing is challenging under strong dependence and heavy tails, since classical Hotelling statistics are ill posed and regularized versions based on sample moments remain sensitive to outliers. This paper develops a robust regularized Hotelling framework for one-sample mean inference under elliptical distributions. The proposed HRST statistic combines a Hettmansperger-Randles spatial location estimator with the inverse of a trace-normalized shrinkage Tyler scatter matrix, and calibrates the resulting quadratic form through ridge-resolvent random-matrix theory rather than sparse covariance or precision-matrix assumptions. In the regime $p/n\to y\in(0,\infty)$, allowing a vanishing lower bulk edge and finite-rank diverging spikes, we establish feasible asymptotic normality for each shrinkage level, derive local-alternative distributions with explicit noncentrality parameters, and prove joint Gaussian limits over finite shrinkage grids. These results justify an adaptive Cauchy combination test across shrinkage levels. Simulations and a paired tumor-normal gene-expression study show that HRST maintains size and improves robustness under heavy-tailed distributions while retaining power under strong correlation.

stat.ME↗

arXiv2026

Two-sample tests for principal eigenvalues and eigenvectors in high-dimensional elliptical factor models

Changes in principal eigenvalues and eigendirections provide complementary diagnostics of structural instability in factor models, but covariance-based inference can be unreliable under heavy tails. We develop two-sample tests for equality of these features of trace-normalized shape matrices under high-dimensional elliptical factor models. Our approach combines Tyler's identity with orthogonalization and cross-fitting to accommodate general location and precision pilots. We derive a spectral limit theory that yields asymptotically valid calibration without upper-tail moment assumptions on the radial variables, allowing the two populations to have different radial distributions and factor ranks. Simulations demonstrate good size control and gains in size-adjusted power over covariance-based benchmarks under heavy-tailed elliptical distributions. An application to S\&P~500 stock returns illustrates how the tests distinguish changes in relative component strength from changes in component orientation.

stat.ME↗

arXiv2026

What Should Federated LoRA Share? FedSAIL via Input-aware Subspace Alignment

Federated low-rank adaptation (LoRA) requires identifying an update structure that is shared across heterogeneous clients. Prior work reports strong similarity among trained LoRA projection matrices across clients; however, such agreement may be largely induced by common initialization and collapses toward random overlap under independent initialization. More crucially, relying solely on parameter similarity inherently ignores the influence of local input regime. To uncover a more robust shared structure, we introduce an input-aware action matrix that weights the adapter update by the second-moment statistics of local layer inputs. Empirically, while parameter similarity vanishes, the leading right singular directions of this action matrix remain strongly aligned across clients. This shared geometry preserves task-conditioned differences and naturally varies across network depths. Motivated by these findings, we propose Federated Subspace-Guided Action-Informed Learning (FedSAIL). Instead of averaging weights, FedSAIL estimates a shared action subspace to regularize local training while preserving client-specific coefficients. Across several benchmarks, our approach consistently improves predictive performance over competing federated LoRA methods while reducing communication cost significantly.

cs.LG↗

arXiv2026

High-Dimensional Two-Sample Inference via Marginal Likelihood-Ratio Rank Statistics

We develop a rank-based framework for high-dimensional two-sample testing that detects marginal distributional differences beyond means and variances. Three marginal likelihood-ratio statistics generate SUM tests for widespread differences, MAX tests for concentrated departures, and Cauchy combinations for unknown signal sparsity. The procedures retain all pooled ranks and impose no moment conditions on continuous margins. For unequal but comparable sample sizes and dimension growing polynomially with their total, we establish normal limits for the studentized SUM statistics and Gumbel limits for the normalized MAX statistics under weak Gaussian-copula dependence. Their within-family asymptotic independence yields standard Cauchy limits for the combinations. The integrated maxima require family-specific centering corrections that accommodate interior, critical, and boundary regimes. Consistency is established under shrinking marginal and aggregate signals, with Cauchy combinations retaining MAX or SUM consistency on specified sparse and dense alternative classes. Simulations examine location, scale, and shape changes, including alternatives preserving the first two moments. Applications to acoustic measurements from a Parkinson's cohort and leukemia gene-expression data illustrate the complementary benefits of SUM and MAX aggregation.

stat.ME↗

arXiv2026

Diagonalized Attention for Individualized Regression: Latent-Row Localization and Prediction

Modern text and image representations are often matrix-valued, with rows corresponding to tokens, patches, or other local feature vectors. Predictive information is often sparse but sample-specific, making classical sparse regression methods with a common support poorly suited to this heterogeneity. This paper formalizes an individualized sparse regression framework for matrix-valued covariates in which each observation has its own rows of interest, while the associated regression effects are shared across the population. To estimate this model, we introduce a diagonalized attention mechanism that uses query--key scores to localize sample-specific signal rows and a value matrix for downstream regression. The proposed method has a parameter dimension independent of sample size and can identify rows of interest for new observations without their responses. We establish existence theorems showing that, under suitable score-separation and concentration conditions, single-head and multi-head diagonalized attention models recover the latent rows with high probability, yielding prediction risk bounds. Our theory therefore provides a statistical explanation of how attention-based scoring localizes sample-specific signals in heterogeneous matrix-valued data. Simulations demonstrate strong prediction and localization in regression and misspecified classification across varying sample sizes, dimensions, and signal cardinalities. Real sentiment analyses show improved classification accuracy and interpretable token selection.

stat.ML↗

arXiv2026

Nonparametric Change-Point Detection and Inference for High-Dimensional Distributions

High-dimensional distributions can change without altering means or covariances, while the number of affected coordinates is often unknown. We propose nonparametric procedures that address both challenges through standardized rank comparisons of marginal distributions. Sum and maximum scans target dense and sparse changes, and a Cauchy combination adapts to unknown sparsity. The procedures require no marginal moment assumptions and extend to multiple-change detection through wild binary segmentation. Under a weakly dependent Gaussian copula model, we establish asymptotic null distributions, asymptotic independence, detection consistency, and localization guarantees. Simulations demonstrate competitive performance for changes in shape and tails, including alternatives that preserve the first two moments. Applications to gene expression and sensor data illustrate the practical benefits of combining dense and sparse evidence.

stat.ME↗

arXiv2026

Learning CNN Filters via Generalized Stein's Method

Convolutional Neural Networks (CNNs) have undoubtedly revolutionized image data analysis and the field of computer vision. As the cornerstone of CNNs, the convolution operation enables the networks to extract abstract features and uncover hidden relationships in the image data. This paper considers the problem of estimating convolution filters from a statistical perspective using a classical tool --- Stein's formula. We first formulate CNNs into a general index model with matrix-valued input, where convolution filters can be viewed as index vectors. Furthermore, we propose a novel singular value decomposition (SVD) based approach to accurately learn the convolution filters based on a generalized version of the first-order Stein's formula. Theoretical analysis suggests that our estimation achieves an optimal convergence rate, comparable to that of generalized linear models where the link function is known. Extensive simulation studies and real data analyses demonstrate that our approach outperforms popular deep learning algorithms, such as Adam. Notably, our method extends beyond filter estimation and can be applied to nonlinear dimension reduction, providing a viable pathway for representation learning.

stat.AP↗

arXiv2026

Spatial-sign-based multilinear principal component analysis for tensor data

Multilinear principal component analysis (MPCA) reduces the dimension of tensor-valued data while preserving their mode-specific structure, but its quadratic scatter criterion can be unstable under heavy-tailed distributions and contamination. We propose spatial-sign-based multilinear principal component analysis (SMPCA), a robust dimension-reduction method that centers the observations by their spatial median, removes radial magnitude through spatial-sign normalization, and estimates the mode-wise loading spaces by alternating eigendecompositions. Under a separable tensor elliptical model, we show that the target mode-wise loading spaces uniquely maximize the population criterion and that one complete sweep of exact population block updates recovers them from any initialization. We also characterize exactly when their tensor-product subspace coincides with a leading unrestricted subspace of vectorized spatial-sign PCA and, when finite second moments exist, ordinary vectorized PCA. At the sample level, we derive explicit statistical rates for the mode-wise subspaces and the joint multilinear projector, obtain corresponding reconstruction guarantees, establish consistency of the cumulative-contribution dimension selector, and prove that the objective values generated by exact cyclic updates are nondecreasing and convergent. Simulations and an empirical application show that SMPCA is more accurate and stable than competitors under heavy-tailed distributions and outlier contamination, while retaining competitive performance under light-tailed settings.

stat.ME↗

arXiv2026

High-Dimensional Data Analysis for Elliptically Symmetric Distributions

High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets exhibit heavy tails, heterogeneity, and departures from classical covariance-based models. This book provides a systematic treatment of high-dimensional data analysis under elliptically symmetric distributions, with an emphasis on robust inference based on spatial signs, spatial ranks, multivariate Kendall's tau matrices, and related shape-based methods.The book covers the basic theory of elliptical symmetry, high-dimensional location inference, estimation and testing for covariance and precision matrices, sphericity and proportionality testing, high-dimensional alpha testing in factor pricing models, change-point analysis, white-noise and independence testing, high-dimensional discriminant analysis, and dimension reduction through principal component analysis and factor models. Throughout, we review classical low-dimensional and high-dimensional benchmark methods and then develop robust alternatives tailored to elliptical models. Particular attention is paid to the interplay between sum-type, max-type, and adaptive procedures, as well as to the role of scatter, shape, and rank-based dependence measures in heavy-tailed settings. This book is intended as a unified overview of robust high-dimensional methods under elliptical symmetry and as a synthesis of the author's recent research contributions in this area. It is written for researchers and graduate students in statistics, econometrics, and related fields who are interested in modern high-dimensional inference beyond the Gaussian paradigm.

stat.ME↗

arXiv2026

Adaptive L-statistics for high dimensional test problem

In this study, we focus on applying L-statistics to the high-dimensional one-sample location test problem. Intuitively, an L-statistic with $k$ parameters tends to perform optimally when the sparsity level of the alternative hypothesis matches $k$. We begin by deriving the limiting distributions for both L-statistics with fixed parameters and those with diverging parameters. To ensure robustness across varying sparsity levels of alternative hypotheses, we first establish the asymptotic independence between L-statistics with fixed and diverging parameters. Building on this, we propose a Cauchy combination test that integrates L-statistics with different parameters. Both simulation results and real-data applications highlight the advantages of our proposed methods.

stat.ME↗

arXiv2026

Factor-Adjusted Location Tests for High-Dimensional Time Series

We study high-dimensional one-sample mean testing for time series with strong common serial dependence driven by latent dynamic factors. After estimating the dynamic factor loading space from lagged autocovariance, we project the data onto its orthogonal complement and construct three factor-adjusted tests: a max test for sparse alternatives, a quadratic test for dense alternatives, and a Cauchy combination test for unknown sparsity. The idiosyncratic component is allowed to be non-Gaussian sub-Gaussian vector white noise. We establish the Gumbel limit of the max statistic, the normal limit and local power function of the quadratic statistic, their asymptotic independence, and the validity of the Cauchy combination. In the strong-factor case, the refined projection expansion shows that the quadratic statistic remains valid for dimensions as large as $p=o(n^2)$. A random-loading residual bootstrap is developed for finite-sample calibration. Simulation studies and a real data application demonstrate reliable size control and competitive power for high-dimensional observations with strong dependence.

stat.ME↗

arXiv2026

Elliptical Regularized Hotelling Tests for High-Dimensional Change-Point Detection

We propose an elliptical regularized Hotelling (ERHT) procedure for detecting location changes in high-dimensional sequences with heavy-tailed, cross-sectionally dependent observations. ERHT contrasts spatial medians on adjacent segments using a ridge-regularized inverse of the pooled centered spatial-sign covariance matrix, thereby combining robustness to radial variation with dependence-aware weighting. We establish Gaussian-process limits for the single- and multiple-change scans and joint convergence over a finite set of regularization parameters. These results provide asymptotically exact calibration of a Cauchy-aggregated adaptive test through the joint Gaussian limit, together with guarantees for local power and single-change localization. We further embed the ERHT score in wild binary segmentation and prove consistency for estimating the number and locations of multiple changes. Simulations show that ERHT is generally well calibrated and delivers competitive power under heavy-tailed distributions, particularly when cross-sectional dependence is substantial. An analysis of the Fama--French 49 industry portfolios reveals persistent evidence of location instability and identifies four structural breaks.

stat.ME↗

arXiv2026

Adaptive Ridge-Regularized Hotelling Change-Point Tests for Functional Data

We propose a unified ridge-regularized Hotelling framework for detecting and locating mean changes in functional time series. A growing basis expansion converts the functional observations into high-dimensional score vectors. Their long-run covariance is estimated by an edge-corrected difference-based procedure. Ridge regularization stabilizes inference under spectral decay. An explicit local-power formula shows that the power-maximizing ridge depends on the unknown spectral orientation of the change. We therefore combine a family of ridge CUSUM statistics by a Cauchy transform and calibrate the aggregate directly from their joint weighted-bridge limit. For multiple changes, we embed local maximum-ridge statistics in a wild binary segmentation procedure, followed by local refinement. Under mild conditions, we establish the validity, local power, consistency, and localization properties of the proposed tests. In the multiple-change setting, the procedure consistently recovers the number of changes and uniformly estimates their locations. The framework accommodates weak dependence and non-Gaussian functional errors. Simulations and two empirical applications demonstrate the favorable finite-sample performance of the proposed methods.

stat.ME↗

arXiv2026

Elliptical Regularized Hotelling Testing for High Dimensional Data

We consider one-sample testing of a high-dimensional location parameter under elliptically symmetric distributions with heavy tails and pervasive cross-sectional dependence. We propose an elliptical regularized Hotelling test with Cauchy combination (ERHT--CC), based on the sample spatial median and the spatial-sign covariance matrix centered at that median. We derive its null asymptotic normality, consistent estimators of the centering and variance, and an explicit local power function. Since the power-optimal ridge parameter depends on the unknown alternative, we aggregate fixed-ridge $p$-values over a deterministic grid using the Cauchy rule. We establish a finite-grid joint Gaussian limit, justify the analytic combined $p$-value without estimating cross-ridge correlations, and characterize its local power. Simulation studies and an empirical analysis demonstrate the favorable finite-sample performance of ERHT--CC under heavy tails and pervasive dependence.

stat.ME↗

arXiv2026

Cauchy Aggregation of Ridge-Regularized Hotelling Tests for High-Dimensional Change-Point Detection

Ridge-regularized Hotelling-type (RHT) change-point tests depend on a ridge parameter $λ$, but the power-optimal value is determined by the unknown covariance structure and the unknown mean shift. We avoid selecting a single ridge value by computing fixed-ridge p-values on a finite deterministic grid and aggregating them with the Cauchy combination rule. Under the standard random-matrix conditions for fixed-ridge RHT statistics, we establish finite-grid joint weak convergence of the ridge processes. This leads to fixed-level validity under joint-limit calibration and small-tail validity for the analytic Cauchy p-value. Monte Carlo experiments show that deterministic-grid Cauchy aggregation has stable size behavior and achieves power close to the best stable fixed ridge choice across a range of covariance and signal configurations.

stat.ME↗