arXiv subjects

Zhaojun Wang

Publications and source records attributed to Zhaojun Wang.

At least 19 recordsLinked to original sources

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.

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arXiv2026

Feedback-Enhanced Online Multiple Testing with Applications to Conformal Selection

This work studies online multiple testing with feedback, where decisions are made sequentially, and the true state of the hypothesis is revealed after decisions are made, either instantly or with a delay, and under either full or bandit feedback. We propose Generalized alpha-investing with feedback (GAIF) along with its adaptive variants, a feedback-enhanced framework that dynamically adjusts thresholds using revealed outcomes, ensuring finite-sample false discovery rate (FDR)/marginal FDR (mFDR) control. We further extend GAIF to online conformal testing by constructing valid conformal $p$-values and developing feedback-enhanced testing rules with finite-sample mFDR control. We also propose a feedback-driven score selection criterion to adaptively choose the candidate score that is most effective for the testing procedure, together with a theoretical analysis of its optimality.} Numerical simulations and real-data applications demonstrate the effectiveness of our methods.

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arXiv2026

Stabilizing black-box algorithms through task-oriented randomization

As black-box models become foundational to modern research, ensuring their stability is paramount for the realization of trustworthy artificial intelligence. The inherent diversity of inputs - ranging from structured Gaussian distributions to complex data with unknown structures - poses a significant challenge: how to stabilize black-box outputs while effectively leveraging available prior information. This paper introduces a task-oriented randomization methodology that adaptively tailors its strategy to the underlying generative mechanisms of the input data, specifically addressing unstructured complexities. A comprehensive suite of stability guarantees is proposed. Beyond establishing rigorous theoretical foundations for stability, the research provides a detailed analysis of the intrinsic trade-off between stability and exploration. Motivated by the architecture of Large Language Models, the framework is further extended to top-k ranking problems. The validity and effectiveness of the proposal are demonstrated through extensive numerical simulations and applications to the real-world dataset.

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arXiv2026

Shape-Adaptive Conditional Calibration for Conformal Prediction via Minimax Optimization

Achieving valid conditional coverage in conformal prediction is challenging due to the theoretical difficulty of satisfying pointwise constraints in finite samples. Building upon the characterization of conditional coverage through marginal moment restrictions, we introduce Minimax Optimization Predictive Inference (MOPI), a framework that generalizes prior work by optimizing over a flexible class of set-valued mappings during the calibration phase, rather than simply calibrating a fixed sublevel set. This minimax formulation effectively circumvents the structural constraints of predefined score functions, achieving superior shape adaptivity while maintaining a principled connection to the minimization of mean squared coverage error. Theoretically, we provide non-asymptotic oracle inequalities and show that the convergence rate of the coverage error attains the optimal order under regular conditions. The MOPI also enables valid inference conditional on sensitive attributes that are available during calibration but unobserved at test time. Empirical results on complex, non-standard conditional distributions demonstrate that MOPI produces more efficient prediction sets than existing baselines.

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arXiv2026

Changepoint Detection in Complex Models: Cross-Fitting Is Needed

Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or hyperparameter tuning -- this strategy can lead to inaccurate changepoint estimation due to over-adaptivity biases. To mitigate this issue, we propose a novel cross-fitting methodology based on out-of-sample loss evaluations, which decouples model fitting from changepoint search. We establish a general theoretical framework for consistent changepoint estimation under mild conditions, and further extend it to temporally dependent data. A key implication of the theory is that consistency depends primarily on the models' predictive accuracy over nearly homogeneous segments. Numerical experiments show that the proposed method substantially improves the reliability and adaptability of changepoint detection in complex scenarios.

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arXiv2026

Testing Alpha in High-Dimensional Conditional Time-Varying Factor Models with Dependent Observations

This paper studies alpha testing in a high-dimensional conditional time-varying factor model with temporally dependent observations. Both factor loadings and alpha processes are allowed to vary smoothly over time, and the cross-sectional dimension may be comparable to or larger than the sample size. Using a B-spline sieve method, we develop a sum-type test for dense alternatives, a max-type test for sparse alternatives, and a Cauchy combination test for adaptive inference. On the theoretical side, we derive explicit stochastic expansions for the estimated average alphas, establish asymptotic normality of the sum statistic, and develop the extreme-value limit theory for the max statistic by showing its Gumbel convergence under temporal dependence together with the validity of block-bootstrap calibration. We further prove asymptotic independence between the sum and max statistics and thereby justify the Cauchy combination test. Simulation results demonstrate that the proposed procedures achieve satisfactory size control and competitive power across a wide range of dense and sparse alternatives. An empirical application further illustrates the usefulness of the proposed methods in testing asset-pricing models with time-varying structure.

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arXiv2026

Conditional Rank-Rank Regression via Deep Conditional Transformation Models

Intergenerational mobility quantifies the transmission of socio-economic outcomes from parents to children. While rank-rank regression (RRR) is standard, adding covariates directly (RRRX) often yields parameters with unclear interpretation. Conditional rank-rank regression (CRRR) resolves this by using covariate-adjusted (conditional) ranks to measure within-group mobility. We improve and extend CRRR by estimating conditional ranks with a deep conditional transformation model (DCTM) and cross-fitting, enabling end-to-end conditional distribution learning with structural constraints and strong performance under nonlinearity, high-order interactions, and discrete ordered outcomes where the distributional regression used in traditional CRRR may be cumbersome or prone to misconfiguration. We further extend CRRR to discrete outcomes via an $ω$-indexed conditional-rank definition and study sensitivity to $ω$. For continuous outcomes, we establish an asymptotic theory for the proposed estimators and verify the validity of exchangeable bootstrap inference. Simulations across simple/complex continuous and discrete ordered designs show clear accuracy gains in challenging settings. Finally, we apply our method to two empirical studies, revealing substantial within-group persistence in U.S. income and pronounced gender differences in educational mobility in India.

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arXiv2025

Aggregating Conformal Prediction Sets via α-Allocation

Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet, efficiently leveraging multiple conformity scores to reduce prediction set size remains a major open challenge. Instead of selecting a single best score, this work introduces a principled aggregation strategy, COnfidence-Level Allocation (COLA), that optimally allocates confidence levels across multiple conformal prediction sets to minimize empirical set size while maintaining provable coverage. Two variants are further developed, COLA-s and COLA-f, which guarantee finite-sample marginal coverage via sample splitting and full conformalization, respectively. In addition, we develop COLA-l, an individualized allocation strategy that promotes local size efficiency while achieving asymptotic conditional coverage. Extensive experiments on synthetic and real-world datasets demonstrate that COLA achieves considerably smaller prediction sets than state-of-the-art baselines while maintaining valid coverage.

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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

Power Enhancement of Permutation-Augmented Partial-Correlation Tests via Fixed-Row Permutations

Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate of interest. We remedy this by fixing a design-driven subset of rows and permuting only the remainder. The fixed rows are chosen by a greedy algorithm that maximizes a lower bound on power. This strategy reduces covariate-permutation collinearity while preserving worst-case Type I error control. Simulations confirm that this refinement maintains nominal size and delivers substantial power gains over original unrestricted permutations, especially in high-collinearity regimes.

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arXiv2025

Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach

Conformal prediction is a powerful tool for constructing prediction intervals for black-box models, providing a finite sample coverage guarantee for exchangeable data. However, this exchangeability is compromised when some entries of the test feature are contaminated, such as in the case of cellwise outliers. To address this issue, this paper introduces a novel framework called detect-then-impute conformal prediction. This framework first employs an outlier detection procedure on the test feature and then utilizes an imputation method to fill in those cells identified as outliers. To quantify the uncertainty in the processed test feature, we adaptively apply the detection and imputation procedures to the calibration set, thereby constructing exchangeable features for the conformal prediction interval of the test label. We develop two practical algorithms, PDI-CP and JDI-CP, and provide a distribution-free coverage analysis under some commonly used detection and imputation procedures. Notably, JDI-CP achieves a finite sample $1-2α$ coverage guarantee. Numerical experiments on both synthetic and real datasets demonstrate that our proposed algorithms exhibit robust coverage properties and comparable efficiency to the oracle baseline.

stat.ML↗

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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arXiv2025

Robust Multi-Source Domain Adaptation under Label Shift

As the volume of data continues to expand, it becomes increasingly common for data to be aggregated from multiple sources. Leveraging multiple sources for model training typically achieves better predictive performance on test datasets. Unsupervised multi-source domain adaptation aims to predict labels of unlabeled samples in the target domain by using labeled samples from source domains. This work focuses on robust multi-source domain adaptation for multi-category classification problems against the heterogeneity of label shift and data contamination. We investigate a domain-weighted empirical risk minimization framework for robust estimation of the target domain's class proportion. Inspired by outlier detection techniques, we propose a refinement procedure within this framework. With the estimated class proportion, robust classifiers for the target domain can be constructed. Theoretically, we study the finite-sample error bounds of the domain-weighted empirical risk minimization and highlight the improvement of the refinement step. Numerical simulations and real-data applications demonstrate the superiority of the proposed method.

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arXiv2025

ART: Distribution-Free and Model-Agnostic Changepoint Detection with Finite-Sample Guarantees

We introduce ART, a distribution-free and model-agnostic framework for changepoint detection that provides finite-sample guarantees. ART transforms independent observations into real-valued scores via a symmetric function, ensuring exchangeability in the absence of changepoints. These scores are then ranked and aggregated to detect distributional changes. The resulting test offers exact Type-I error control, agnostic to specific distributional or model assumptions. Moreover, ART seamlessly extends to multi-scale settings, enabling robust multiple changepoint estimation and post-detection inference with finite-sample error rate control. By locally ranking the scores and performing aggregations across multiple prespecified intervals, ART identifies changepoint intervals and refines subsequent inference while maintaining its distribution-free and model-agnostic nature. This adaptability makes ART as a reliable and versatile tool for modern changepoint analysis, particularly in high-dimensional data contexts and applications leveraging machine learning methods.

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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

Robust Mutual Fund Selection with False Discovery Rate Control

In this article, we address the challenge of identifying skilled mutual funds among a large pool of candidates, utilizing the linear factor pricing model. Assuming observable factors with a weak correlation structure for the idiosyncratic error, we propose a spatial-sign based multiple testing procedure (SS-BH). When latent factors are present, we first extract them using the elliptical principle component method (He et al. 2022) and then propose a factor-adjusted spatial-sign based multiple testing procedure (FSS-BH). Simulation studies demonstrate that our proposed FSS-BH procedure performs exceptionally well across various applications and exhibits robustness to variations in the covariance structure and the distribution of the error term. Additionally, real data application further highlights the superiority of the FSS-BH procedure.

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arXiv2024

Adaptive Sphericity Tests for High Dimensional Data

In this paper, we investigate sphericity testing in high-dimensional settings, where existing methods primarily rely on sum-type test procedures that often underperform under sparse alternatives. To address this limitation, we propose two max-type test procedures utilizing the sample covariance matrix and the sample spatial-sign covariance matrix, respectively. Furthermore, we introduce two Cauchy combination test procedures that integrate both sum-type and max-type tests, demonstrating their superiority across a wide range of sparsity levels in the alternative hypothesis. Our simulation studies corroborate these findings, highlighting the enhanced performance of our proposed methodologies in high-dimensional sphericity testi

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arXiv2024

On the reducibility of scalar generalized Verma modules associated to two-step nilpotent parabolic subalgebras

Let $\mathfrak{g}$ be a simple complex Lie algebra.A generalized Verma module induced from a one-dimensional representation of a parabolic subalgebra of $\mathfrak{g}$ is called a scalar generalized Verma module of $\mathfrak{g}$. In this article, we use Gelfand-Kirillov dimension to determine the reducibility of scalar generalized Verma modules of $\mathfrak{g}$ associated to a two-step nilpotent parabolic subalgebra of non-maximal type. Such a module exists only when $\mathfrak{g}=\mathfrak{sl}(n,\mathbb{C})$, $\mathfrak{so}(2n,\mathbb{C})$ or $E_6$. We find that the reducible points of these modules can be drawn in a two-dimensional complex plane.

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