arXiv subjects

Xinghao Qiao

Publications and source records attributed to Xinghao Qiao.

At least 19 recordsLinked to original sources

arXiv2026

On Robust Empirical Likelihood for Nonparametric Regression with Application to Regression Discontinuity Designs

Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these settings using local linear smoothers, with Wilks' theorem holding only when an undersmoothed bandwidth is selected. However, the generalization of bias-corrected versions of empirical likelihood under more realistic conditions is non-trivial and has remained an open challenge in the literature. This paper provides a satisfactory solution by proposing a novel approach, referred to as robust empirical likelihood, designed for nonparametric regression and RDD. The core idea is to construct robust weights which simultaneously achieve bias correction and account for the additional variability introduced by the estimated bias, thereby enabling valid confidence interval construction without extra estimation steps involved. We demonstrate that the Wilks' phenomenon still holds under weaker conditions in nonparametric regression, sharp and fuzzy RDD settings. Extensive simulation studies confirm the effectiveness of our proposed approach, showing superior performance over existing methods in terms of coverage probabilities and interval lengths. Moreover, the proposed procedure exhibits robustness to bandwidth selection, making it a flexible and reliable tool for empirical analyses. The practical usefulness is further illustrated through applications to two real datasets.

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arXiv2026

Testing for functional white noise in high dimensions

White noise testing is a fundamental problem in time series analysis. Yet it remains largely unsolved for high-dimensional functional time series, despite the growing attention this area has received in recent years, as existing tests are confined to either univariate functional time series or high-dimensional scalar time series. In this paper, we develop a general error-contamination framework for testing white noise in high-dimensional functional time series. We propose a supremum-type test statistic based on cross-autocovariance functions and develop a parametric bootstrap procedure to approximate its null distribution. By imposing a general high-level condition, we derive a new Gaussian approximation result that ensures size control, and establish an asymptotic power guarantee. We then apply our framework to two concrete applications: (i) white noise test for discretely observed functional time series, and (ii) residual-based goodness-of-fit test for functional factor model. For each problem, we verify the corresponding high-level condition to ensure the theoretical validity of our proposed method. Extensive simulations show that our proposed method achieves good finite-sample performance. The practical utility of our proposed method is further illustrated through applications to two real datasets.

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arXiv2026

Weight-calibrated estimation for factor models of high-dimensional time series

The factor modeling for high-dimensional time series is powerful in discovering latent common components for dimension reduction and information extraction. Most available estimation methods can be divided into two categories: the covariance-based under asymptotically-identifiable assumption and the autocovariance-based with white idiosyncratic noise. This paper follows the autocovariance-based framework and develops a novel weight-calibrated method to improve the estimation performance. It adopts a linear projection to tackle high-dimensionality, and employs a reduced-rank autoregression formulation. The asymptotic theory of the proposed method is established, relaxing the assumption on white noise. Additionally, we make the first attempt in the literature by providing a systematic theoretical comparison among the covariance-based, the standard autocovariance-based, and our proposed weight-calibrated autocovariance-based methods in the presence of factors with different strengths. Extensive simulations are conducted to showcase the superior finite-sample performance of our proposed method, as well as to validate the newly established theory. The superiority of our proposal is further illustrated through the analysis of one financial and one macroeconomic data sets.

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arXiv2026

Time Series Gaussian Chain Graph Models

Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned blockwise dependence, with distinct patterns within and across blocks. In this paper, we introduce a new class of time series Gaussian chain graph models that represent contemporaneous and lagged causal relations via directed edges across blocks, while capturing within-block conditional dependencies through undirected edges. In the frequency domain, this formulation induces a cross-frequency shared group sparse plus group low-rank decomposition of the inverse spectral density matrices, which we exploit to establish identifiability of the time series chain graph structure. Building on this, we then propose a three-stage learning procedure for estimating the undirected and directed edge sets, which involves optimizing a regularized Whittle likelihood with a group lasso penalty to encourage group sparsity and a novel tensor-unfolding nuclear norm penalty to enforce group low-rank structure. We investigate the asymptotic properties of the proposed method, ensuring its consistency for exact recovery of the chain graph structure. The superior empirical performance of the proposed method is demonstrated through both extensive simulation studies and an application to U.S. macroeconomic data that highlights key monetary policy transmission mechanisms.

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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.

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arXiv2025

Factor-guided estimation of large covariance matrix function with conditional functional sparsity

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar loadings or scalar factors with functional loadings, and postulate functional sparsity on the covariance of idiosyncratic errors after taking out the common unobserved factors. To facilitate estimation, we rely on the spiked matrix model and its functional generalization, and derive some novel asymptotic identifiability results, based on which we develop DIGIT and FPOET estimators under two functional factor models, respectively. Both estimators involve performing associated eigenanalysis to estimate the covariance of common components, followed by adaptive functional thresholding applied to the residual covariance. We also develop functional information criteria for model selection with theoretical guarantees. The convergence rates of involved estimated quantities are respectively established for DIGIT and FPOET estimators. Numerical studies including extensive simulations and a real data application on functional portfolio allocation are conducted to examine the finite-sample performance of the proposed methodology.

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arXiv2025

On a new robust method of inference for general time series models

In this article, we propose a novel logistic quasi-maximum likelihood estimation (LQMLE) for general parametric time series models. Compared to the classical Gaussian QMLE and existing robust estimations, it enjoys many distinctive advantages, such as robustness in respect of distributional misspecification and heavy-tailedness of the innovation, more resiliency to outliers, smoothness and strict concavity of the log logistic quasi-likelihood function, and boundedness of the influence function among others. Under some mild conditions, we establish the strong consistency and asymptotic normality of the LQMLE. Moreover, we propose a new and vital parameter identifiability condition to ensure desirable asymptotics of the LQMLE. Further, based on the LQMLE, we consider the Wald test and the Lagrange multiplier test for the unknown parameters, and derive the limiting distributions of the corresponding test statistics. The applicability of our methodology is demonstrated by several time series models, including DAR, GARCH, ARMA-GARCH, DTARMACH, and EXPAR. Numerical simulation studies are carried out to assess the finite-sample performance of our methodology, and an empirical example is analyzed to illustrate its usefulness.

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arXiv2025

Large covariance matrix estimation with factor-assisted variable clustering

This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse error covariance matrix after taking out common factors may be invalid for many financial applications. Our formulation postulates a latent model-based error cluster structure after removing observable factors, which not only leads to more interpretable cluster patterns but also accounts for non-sparse cross-sectional correlations among the variable-specific residuals. Our method begins with using least-squares to estimate the factor loadings, followed by identifying the latent cluster structure by thresholding the scaled covariance difference measures of residuals. A novel ratio-based criterion is introduced to determine the threshold parameter when performing the developed clustering algorithm. We then establish the cluster recovery consistency of our method and derive the convergence rates of our proposed covariance matrix estimators under different norms. Finally, we demonstrate the superior finite sample performance of our proposal over the competing methods through both extensive simulations and a real data application on minimum variance portfolio.

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arXiv2025

From sparse to dense functional data in high dimensions: Revisiting phase transitions from a non-asymptotic perspective

Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties of the estimation, which reveal interesting phase transition phenomena based on the relative order of the average sampling frequency per subject $T$ to the number of subjects $n$, partitioning the data into three categories: "sparse", "semi-dense", and "ultra-dense". In an increasingly available high-dimensional scenario, where the number of functional variables $p$ is large in relation to $n$, we revisit this open problem from a non-asymptotic perspective by deriving comprehensive concentration inequalities for the local linear smoothers. Besides being of interest by themselves, our non-asymptotic results lead to elementwise maximum rates of $L_2$ convergence and uniform convergence serving as a fundamentally important tool for further convergence analysis when $p$ grows exponentially with $n$ and possibly $T$. With the presence of extra $\log p$ terms to account for the high-dimensional effect, we then investigate the scaled phase transitions and the corresponding elementwise maximum rates from sparse to semi-dense to ultra-dense functional data in high dimensions. We also discuss a couple of applications of our theoretical results. Finally, numerical studies are carried out to confirm the established theoretical properties.

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arXiv2024

Large-scale Multiple Testing of Cross-covariance Functions with Applications to Functional Network Models

The estimation of functional networks through functional covariance and graphical models have recently attracted increasing attention in settings with high dimensional functional data, where the number of functional variables p is comparable to, and maybe larger than, the number of subjects. However, the existing methods all depend on regularization techniques, which make it unclear how the involved tuning parameters are related to the number of false edges. In this paper, we first reframe the functional covariance model estimation as a tuning-free problem of simultaneously testing p(p-1)/2 hypotheses for cross-covariance functions, and introduce a novel multiple testing procedure. We then explore the multiple testing procedure under a general error-contamination framework and establish that our procedure can control false discoveries asymptotically. Additionally, we demonstrate that our proposed methods for two concrete examples: the functional covariance model for discretely observed functional data and, importantly, the more challenging functional graphical model, can be seamlessly integrated into the general error-contamination framework, and, with verifiable conditions, achieve theoretical guarantees on effective false discovery control. Finally, we showcase the superiority of our proposals through extensive simulations and brain connectivity analysis of two neuroimaging datasets.

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arXiv2024

Deep Functional Factor Models: Forecasting High-Dimensional Functional Time Series via Bayesian Nonparametric Factorization

This paper introduces the Deep Functional Factor Model (DF2M), a Bayesian nonparametric model designed for analysis of high-dimensional functional time series. DF2M is built upon the Indian Buffet Process and the multi-task Gaussian Process, incorporating a deep kernel function that captures non-Markovian and nonlinear temporal dynamics. Unlike many black-box deep learning models, DF2M offers an explainable approach to utilizing neural networks by constructing a factor model and integrating deep neural networks within the kernel function. Additionally, we develop a computationally efficient variational inference algorithm to infer DF2M. Empirical results from four real-world datasets demonstrate that DF2M provides better explainability and superior predictive accuracy compared to conventional deep learning models for high-dimensional functional time series.

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arXiv2024

Factor modelling for high-dimensional functional time series

Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables $p$ diverges as the number of serially dependent observations $n$ increases. In this paper, we present a novel functional factor model for high-dimensional functional time series that maintains and makes use of the functional and dynamic structure to achieve great dimension reduction and find the latent factor structure. To estimate the number of functional factors and the factor loadings, we propose a fully functional estimation procedure based on an eigenanalysis for a nonnegative definite and symmetric matrix. Our proposal involves a weight matrix to improve the estimation efficiency and tackle the issue of heterogeneity, the rationale of which is illustrated by formulating the estimation from a novel regression perspective. Asymptotic properties of the proposed method are studied when $p$ diverges at some polynomial rate as $n$ increases. To provide a parsimonious model and enhance interpretability for near-zero factor loadings, we impose sparsity assumptions on the factor loading space and then develop a regularized estimation procedure with theoretical guarantees when $p$ grows exponentially fast relative to $n.$ Finally, we demonstrate that our proposed estimators significantly outperform the competing methods through both simulations and applications to a U.K. temperature data set and a Japanese mortality data set.

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arXiv2024

Functional knockoffs selection with applications to functional data analysis in high dimensions

The knockoffs is a recently proposed powerful framework that effectively controls the false discovery rate (FDR) for variable selection. However, none of the existing knockoff solutions are directly suited to handle multivariate or high-dimensional functional data, which has become increasingly prevalent in various scientific applications. In this paper, we propose a novel functional model-X knockoffs selection framework tailored to sparse high-dimensional functional models, and show that our proposal can achieve the effective FDR control for any sample size. Furthermore, we illustrate the proposed functional model-X knockoffs selection procedure along with the associated theoretical guarantees for both FDR control and asymptotic power using examples of commonly adopted functional linear additive regression models and the functional graphical model. In the construction of functional knockoffs, we integrate essential components including the correlation operator matrix, the Karhunen-Loève expansion, and semidefinite programming, and develop executable algorithms. We demonstrate the superiority of our proposed methods over the competitors through both extensive simulations and the analysis of two brain imaging datasets.

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arXiv2024

On the modelling and prediction of high-dimensional functional time series

We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series $p$ is large in relation to the length of time series $n$. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from any two different groups are uncorrelated both contemporaneously and serially. Consequently in our second step those groups are handled separately without the information loss on the overall linear dynamic structure. The second step is devoted to establishing a finite-dimensional dynamical structure for all the transformed functional time series within each group. Furthermore the finite-dimensional structure is represented by that of a vector time series. Modelling and forecasting for the original high-dimensional functional time series are realized via those for the vector time series in all the groups. We investigate the theoretical properties of our proposed methods, and illustrate the finite-sample performance through both extensive simulation and two real datasets.

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arXiv2023

EEGNN: Edge Enhanced Graph Neural Network with a Bayesian Nonparametric Graph Model

Training deep graph neural networks (GNNs) poses a challenging task, as the performance of GNNs may suffer from the number of hidden message-passing layers. The literature has focused on the proposals of {over-smoothing} and {under-reaching} to explain the performance deterioration of deep GNNs. In this paper, we propose a new explanation for such deteriorated performance phenomenon, {mis-simplification}, that is, mistakenly simplifying graphs by preventing self-loops and forcing edges to be unweighted. We show that such simplifying can reduce the potential of message-passing layers to capture the structural information of graphs. In view of this, we propose a new framework, edge enhanced graph neural network (EEGNN). EEGNN uses the structural information extracted from the proposed Dirichlet mixture Poisson graph model (DMPGM), a Bayesian nonparametric model for graphs, to improve the performance of various deep message-passing GNNs. We propose a Markov chain Monte Carlo inference framework for DMPGM. Experiments over different datasets show that our method achieves considerable performance increase compared to baselines.

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arXiv2022

An autocovariance-based learning framework for high-dimensional functional time series

Many scientific and economic applications involve the statistical learning of high-dimensional functional time series, where the number of functional variables is comparable to, or even greater than, the number of serially dependent functional observations. In this paper, we model observed functional time series, which are subject to errors in the sense that each functional datum arises as the sum of two uncorrelated components, one dynamic and one white noise. Motivated from the fact that the autocovariance function of observed functional time series automatically filters out the noise term, we propose a three-step procedure by first performing autocovariance-based dimension reduction, then formulating a novel autocovariance-based block regularized minimum distance estimation framework to produce block sparse estimates, and based on which obtaining the final functional sparse estimates. We investigate theoretical properties of the proposed estimators, and illustrate the proposed estimation procedure via three sparse high-dimensional functional time series models. We demonstrate via both simulated and real datasets that our proposed estimators significantly outperform the competitors.

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arXiv2022

Adaptive Functional Thresholding for Sparse Covariance Function Estimation in High Dimensions

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the number of random functions p is comparable to, or even larger than the sample size n. Aided by the Hilbert--Schmidt norm of functions, we introduce a new class of functional thresholding operators that combine functional versions of thresholding and shrinkage, and propose the adaptive functional thresholding estimator by incorporating the variance effects of individual entries of the sample covariance function into functional thresholding. To handle the practical scenario where curves are partially observed with errors, we also develop a nonparametric smoothing approach to obtain the smoothed adaptive functional thresholding estimator and its binned implementation to accelerate the computation. We investigate the theoretical properties of our proposals when p grows exponentially with n under both fully and partially observed functional scenarios. Finally, we demonstrate that the proposed adaptive functional thresholding estimators significantly outperform the competitors through extensive simulations and the functional connectivity analysis of two neuroimaging datasets.

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arXiv2022

CATVI: Conditional and Adaptively Truncated Variational Inference for Hierarchical Bayesian Nonparametric Models

Current variational inference methods for hierarchical Bayesian nonparametric models can neither characterize the correlation structure among latent variables due to the mean-field setting, nor infer the true posterior dimension because of the universal truncation. To overcome these limitations, we propose the conditional and adaptively truncated variational inference method (CATVI) by maximizing the nonparametric evidence lower bound and integrating Monte Carlo into the variational inference framework. CATVI enjoys several advantages over traditional methods, including a smaller divergence between variational and true posteriors, reduced risk of underfitting or overfitting, and improved prediction accuracy. Empirical studies on three large datasets reveal that CATVI applied in Bayesian nonparametric topic models substantially outperforms competing models, providing lower perplexity and clearer topic-words clustering.

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