arXiv subjects

Weichi Wu

Publications and source records attributed to Weichi Wu.

At least 19 recordsLinked to original sources

arXiv2026

ConquerNet: Convolution-Smoothed Quantile ReLU Neural Networks with Minimax Guarantees

Quantile regression is a fundamental tool for distributional learning but poses significant optimization challenges for deep models due to the non-smoothness of the pinball loss. We propose ConquerNet, a class of \textbf{con}volution-smoothed \textbf{qu}antil\textbf{e} \textbf{R}eLU neural \textbf{net}works, which yield smooth objectives while preserving the underlying quantile structure. We establish general nonasymptotic risk bounds for ConquerNet under mild conditions, providing minimax guarantees over Besov function classes. In numerical studies, we demonstrate that the proposed approach outperforms standard quantile neural networks at multiple quantile levels, showing improved estimation accuracy and training efficiency across the board, with particularly pronounced advantages at high and low quantiles.

stat.ML↗

arXiv2026

Complex trend inference for high-dimensional piecewise locally stationary time series

This paper studies high-dimensional trend inference for piecewise smooth signals under nonstationary noise and asynchronous structural breaks by first detecting asynchronous changes without assuming stationarity and then further exploiting latent group structures to estimate trend functions. In the first step, we propose AJDN (Asynchronous Jump Detection under Nonstationary Noise), a multiscale framework for the identification and localization of jumps in high-dimensional time series. We show that AJDN consistently recovers the number of jumps with a prescribed asymptotic probability and achieves nearly optimal localization rates in the presence of asynchronicity and nonstationarity, both of which often violate the assumptions of existing high-dimensional change point methods and thereby deteriorate their performance. In the second step, we augment AJDN with a homogeneity pursuit step and obtain AJDN-H, which identifies latent groups of dimensions that share common jump structures and trend parameters given the detected jumps. This allows for efficient information pooling and improves the accuracy of trend estimation under both asynchronicity and nonstationarity. The robustness and finite-sample performance of the proposed methodology are examined by extensive simulation studies. An application to financial data demonstrates the practical utility of the AJDN-H framework in complex, high-dimensional settings.

stat.ME↗

arXiv2026

Low-Rank Graphon Learning for Networks

Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix and a low-rank graphon--two goals rarely achieved jointly. Our method resolves identification issues and enables an efficient sequential algorithm based on subgraph counts and interpolation. We establish consistency and demonstrate strong empirical performance in terms of computational efficiency and estimation accuracy through simulations and data analysis.

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arXiv2025

Convergence of covariance and spectral density estimates for high-dimensional functional time series

Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the number of functional variables is large relative to the length of functional time series, non-asymptotic theory for covariance function estimation has been developed for Gaussian and sub-Gaussian functional linear processes. However, corresponding non-asymptotic results for high-dimensional non-Gaussian and nonlinear functional time series, as well as for spectral density function estimation, are largely unexplored. In this paper, we introduce novel functional dependence measures, based on which we establish systematic non-asymptotic concentration bounds for estimates of (auto)covariance and spectral density functions in high-dimensional and non-Gaussian settings. We then illustrate the usefulness of our convergence results through two applications to dynamic functional principal component analysis and sparse spectral density function estimation. To handle the practical scenario where curves are discretely observed with errors, we further develop convergence rates of the corresponding estimates obtained via a nonparametric smoothing method. Finally, extensive simulation studies are conducted to corroborate our theoretical findings.

math.ST↗

arXiv2025

Asymptotic Uniform False Discovery Rate Control for Inference of Time-varying Correlations

Inference for locally stationary time series is challenging because the associated hypotheses form an uncountable collection over a continuous time interval, making pointwise false discovery rate (FDR) control inadequate for simultaneous statistical guarantees. We introduce a novel asymptotically uniform false discovery rate (AuFDR), defined as the expectation of the $L_r$-norm of the false discovery proportion (FDP) process where $r$ is allowed to diverge, to quantify and control false discoveries uniformly over time. To operationalize AuFDR control, we develop an inferential framework for time-varying correlations in high-dimensional nonstationary time series that allows for non-Gaussianity, nonlinearity and possible jumps in mean functions. The proposed approach combines robust difference-based estimators with a multiplier-bootstrap procedure to construct uniformly valid time-varying $P$-values. Based on these $P$-values, we propose a time-varying Benjamini--Yekutieli procedure for controlling the AuFDR under arbitrary dependence and establish its asymptotic validity. Extensive simulations demonstrate the finite-sample performance of the proposed method in controlling the AuFDR. Applications to EEG data and financial time-series data illustrate its practical utility.

stat.ME↗

arXiv2025

Simultaneous inference for monotone and smoothly time-varying functions under complex temporal dynamics

We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics. This will be done utilizing the monotone rearrangement and the nonparametric estimation. We capitalize the Gaussian approximation for the nonparametric monotone estimator and construct the asymptotically correct simultaneous confidence bands (SCBs) using designed bootstrap methods. We investigate two general and practical scenarios. The first is the simultaneous inference of monotone smooth trends from moderately high-dimensional time series. The proposed algorithm has been employed for the joint inference of temperature curves from multiple areas. Specifically, most existing methods are designed for a single monotone smooth trend. In such cases, our proposed SCB empirically exhibits the narrowest width among existing approaches while maintaining confidence levels. It has also been used for testing several hypotheses tailored to global warming. The second scenario involves simultaneous inference of monotone and smoothly time-varying regression coefficients in time-varying coefficient linear models. The proposed algorithm has been utilized for testing the impact of sunshine duration on temperature which is believed to be increasing due to severe greenhouse effect. The validity of the proposed methods has been justified in theory as well as by extensive simulations.

math.ST↗

arXiv2025

Bayesian online collective anomaly and change point detection in fine-grained time series

Fine-grained time series data are crucial for accurate and timely online change detection. While both collective anomalies and change points can coexist in such data, their joint online detection has received limited attention. In this research, we develop a Bayesian framework capturing time series with collective anomalies and change points, and introduce a recursive online inference algorithm to detect the most recent collective anomaly and change point jointly. For scaling, we further propose an algorithm enhanced with collective anomaly removal that effectively reduces the time and space complexity to linear. We demonstrate the effectiveness of our approach via extensive experiments on simulated data and two real-world applications.

stat.ME↗

arXiv2025

Causal Inference under Interference: Regression Adjustment and Optimality

In randomized controlled trials without interference, regression adjustment is widely used to enhance the efficiency of treatment effect estimation. This paper extends this efficiency principle to settings with network interference, where a unit's response may depend on the treatments assigned to its neighbors in a network. We make three key contributions: (1) we establish a central limit theorem for a linear regression-adjusted estimator and prove its optimality in achieving the smallest asymptotic variance within a class of linear adjustments; (2) we develop a novel, consistent estimator for the asymptotic variance of this linear estimator; and (3) we propose a nonparametric estimator that integrates kernel smoothing and trimming techniques, demonstrating its asymptotic normality and its optimality in minimizing asymptotic variance within a broader class of nonlinear adjustments. Extensive simulations validate the superior performance of our estimators, and a real-world data application illustrates their practical utility. Our findings underscore the power of regression-based methods and reveal the potential of kernel-and-trimming-based approaches for further enhancing efficiency under network interference.

stat.ME↗

arXiv2024

A portmanteau test for multivariate non-stationary functional time series with an increasing number of lags

Multivariate locally stationary functional time series provide a flexible framework for modeling functional data exhibiting both temporal and spatial dependencies while allowing for a time-varying data generating mechanism. In this paper, we introduce a portmanteau-type test for assessing white noise assumptions tailored for multivariate locally stationary functional time series without dimension reduction. A simple bootstrap procedure is proposed to implement the test, because it is not clear if the limiting distribution of the test statistic exists. Our approach is based on a Gaussian approximation result for a degenerate $U$-statistic of second-order functional time series involving an increasing number of lags, which is of independent interest. Through theoretical analysis, simulation studies, and real data analysis of energy consumptions, we demonstrate the efficacy and adaptability of the proposed method in detecting departures from white noise assumptions in multivariate locally stationary functional time series. Finally, the R package corresponding to our method can be downloaded from https://github.com/Lujia-Bai/nftsport.

stat.ME↗

arXiv2024

Confidence surfaces for the mean of locally stationary functional time series

The problem of constructing a simultaneous confidence surface for the 2-dimensional mean function of a non-stationary functional time series is challenging as these bands can not be built on classical limit theory for the maximum absolute deviation between an estimate and the time-dependent regression function. In this paper, we propose a new bootstrap methodology to construct such a region. Our approach is based on a Gaussian approximation for the maximum norm of sparse high-dimensional vectors approximating the maximum absolute deviation which is suitable for nonparametric inference of high-dimensional time series. The elimination of the zero entries produces (besides the time dependence) additional dependencies such that the "classical" multiplier bootstrap is not applicable. To solve this issue we develop a novel multiplier bootstrap, where blocks of the coordinates of the vectors are multiplied with random variables, which mimic the specific structure between the vectors appearing in the Gaussian approximation. We prove the validity of our approach by asymptotic theory, demonstrate good finite sample properties by means of a simulation study and illustrate its applicability by analyzing a data example.

math.ST↗

arXiv2024

Random Interval Distillation for Detection of Change-Points in Markov Chain Bernoulli Networks

We propose a new and generic approach for detecting multiple change-points in dynamic networks with Markov formation, termed random interval distillation (RID). By collecting random intervals with sufficient strength of signals and reassembling them into a sequence of informative short intervals, together with sparse universal singular value thresholding, our new approach can achieve nearly minimax optimality as their independent counterparts for both detection and localization bounds in low-rank networks without any prior knowledge about minimal spacing, which is unlike many previous methods. In particular, motivated by a recent nonasymptotic bound, our method uses the operator norm of CUSUMs of the adjacency matrices, and achieves the aforementioned optimality without sample splitting as required by the previous method. For practical applications, we introduce a clustering-based and data-driven procedure to determine the optimal threshold for signal strength, utilizing the connection between RID and clustering. We examine the effectiveness and usefulness of our methodology via simulations and a real data example.

stat.ME↗

arXiv2024

Difference-based covariance matrix estimate in time series nonparametric regression with applications to specification tests

Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt structural breaks and its competitive finite sample performance. However, existing methods mainly focus on estimators for the univariate process while their direct and multivariate extensions for most linear models are asymptotically biased. We propose a novel difference-based and debiased long-run covariance matrix estimator for functional linear models with time-varying regression coefficients, allowing time series non-stationarity, long-range dependence, state-heteroscedasticity and their mixtures. We apply the new estimator to (i) the structural stability test, overcoming the notorious non-monotonic power phenomena caused by piecewise smooth alternatives for regression coefficients, and (ii) the nonparametric residual-based tests for long memory, improving the performance via the residual-free formula of the proposed estimator. The effectiveness of the proposed method is justified theoretically and demonstrated by superior performance in simulation studies, while its usefulness is elaborated via real data analysis. Our method is implemented in the R package mlrv.

stat.ME↗

arXiv2024

Adaptive Estimation for Non-stationary Factor Models And A Test for Static Factor Loadings

This paper considers the estimation and testing of a class of locally stationary time series factor models with evolutionary temporal dynamics. In particular, the entries and the dimension of the factor loading matrix are allowed to vary with time while the factors and the idiosyncratic noise components are locally stationary. We propose an adaptive sieve estimator for the span of the varying loading matrix and the locally stationary factor processes. A uniformly consistent estimator of the effective number of factors is investigated via eigenanalysis of a non-negative definite time-varying matrix. A possibly high-dimensional bootstrap-assisted test for the hypothesis of static factor loadings is proposed by comparing the kernels of the covariance matrices of the whole time series with their local counterparts. We examine our estimator and test via simulation studies and real data analysis. Finally, all our results hold at the following popular but distinct assumptions: (a) the white noise idiosyncratic errors with either fixed or diverging dimension, and (b) the correlated idiosyncratic errors with diverging dimension.

stat.ME↗

arXiv2023

Multiscale Jump Testing and Estimation Under Complex Temporal Dynamics

We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed to diverge to infinity with the jump sizes possibly shrinking to zero. The method is based on a multiscale application of an optimal jump-pass filter to the time series, where the scales are dense between admissible lower and upper bounds. For a wide class of non-stationary time series models and trend functions, the proposed method is shown to be able to detect all jump points within a nearly optimal range with a prescribed probability asymptotically under mild conditions. For a time series of length $n$, the computational complexity of the proposed method is $O(n)$ for each scale and $O(n\log^{1+ε} n)$ overall, where $ε$ is an arbitrarily small positive constant. Numerical studies show that the proposed jump testing and estimation method performs robustly and accurately under complex temporal dynamics.

stat.ME↗

arXiv2023

A Random Graph-based Autoregressive Model for Networked Time Series

Contemporary time series data often feature objects connected by a social network that naturally induces temporal dependence involving connected neighbours. The network vector autoregressive model is useful for describing the influence of linked neighbours, while recent generalizations aim to separate influence and homophily. Existing approaches, however, require either correct specification of a time series model or accurate estimation of a network model or both, and rely exclusively on least-squares for parameter estimation. This paper proposes a new autoregressive model incorporating a flexible form for latent variables used to depict homophily. We develop a first-order differencing method for the estimation of influence requiring only the influence part of the model to be correctly specified. When the part including homophily is correctly specified admitting a semiparametric form, we leverage and generalize the recent notion of neighbour smoothing for parameter estimation, bypassing the need to specify the generative mechanism of the network. We develop new theory to show that all the estimated parameters are consistent and asymptotically normal. The efficacy of our approach is confirmed via extensive simulations and an analysis of a social media dataset.

stat.ME↗

arXiv2023

Detecting long-range dependence for time-varying linear models

We consider the problem of testing for long-range dependence in time-varying coefficient regression models, where the covariates and errors are locally stationary, allowing complex temporal dynamics and heteroscedasticity. We develop KPSS, R/S, V/S, and K/S-type statistics based on the nonparametric residuals. Under the null hypothesis, the local alternatives as well as the fixed alternatives, we derive the limiting distributions of the test statistics. As the four types of test statistics could degenerate when the time-varying mean, variance, long-run variance of errors, covariates, and the intercept lie in certain hyperplanes, we show the bootstrap-assisted tests are consistent under both degenerate and non-degenerate scenarios. In particular, in the presence of covariates the exact local asymptotic power of the bootstrap-assisted tests can enjoy the same order as that of the classical KPSS test of long memory for strictly stationary series. The asymptotic theory is built on a new Gaussian approximation technique for locally stationary long-memory processes with short-memory covariates, which is of independent interest. The effectiveness of our tests is demonstrated by extensive simulation studies and real data analysis.

math.ST↗

arXiv2023

Time-varying correlation network analysis of non-stationary multivariate time series with complex trends

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonparametric estimators of cross-correlations, achieve accurate family-wise error control via a bootstrap-assisted procedure adaptive to the complex temporal dynamics, and enhance the probability of recovering the time-varying network structures using a new uniform variance reduction technique. We prove the asymptotic validity of the proposed method and demonstrate its effectiveness in finite samples through simulation studies and empirical applications.

stat.ME↗

arXiv2021

Shift identification in time varying regression quantiles

This article investigates whether time-varying quantile regression curves are the same up to the horizontal shift or not. The errors and the covariates involved in the regression model are allowed to be locally stationary. We formalize this issue in a corresponding non-parametric hypothesis testing problem, and develop an integrated-squared-norm based test (SIT) as well as a simultaneous confidence band (SCB) approach. The asymptotic properties of SIT and SCB under null and local alternatives are derived. Moreover, the asymptotic properties of these tests are also studied when the compared data sets are dependent. We then propose valid wild bootstrap algorithms to implement SIT and SCB. Furthermore, the usefulness of the proposed methodology is illustrated via analysing simulated and real data related to COVID-19 outbreak and climate science.

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