arXiv subjects

Wenya Luo

Publications and source records attributed to Wenya Luo.

5 recordsLinked to original sources

arXiv2026

Transfer Learning for Linear Discriminant Analysis with a Shared Classification Signal

This paper studies transfer learning for linear discriminant analysis in high-dimensional two-class classification. We consider one target domain and several source domains, where the mean difference in each domain is decomposed into a deterministic common component and a domain-specific random deviation. The common component represents a shared classification signal across domains, while the random deviation captures domain-specific heterogeneity. Under spiked covariance models, we derive deterministic limits for the target-domain Gaussian-calibrated error of weighted transfer classifiers under both homogeneous and heterogeneous covariance settings. These limits quantify the effects of the shared signal, domain-specific variation, dimension-to-sample-size ratios, and spike structures on transfer performance. They further lead to oracle transfer weights and consistent data-driven plug-in estimators. We also characterize the intercept bias induced by unbalanced target-domain class sample sizes and provide an asymptotically optimal correction.

stat.ME↗

arXiv2025

Spectrally-Corrected and Regularized QDA Classifier for Spiked Covariance Model

Quadratic discriminant analysis (QDA) is a widely used method for classification problems, particularly preferable over Linear Discriminant Analysis (LDA) for heterogeneous data. However, QDA loses its effectiveness in high-dimensional settings, where the data dimension and sample size tend to infinity. To address this issue, we propose a novel QDA method utilizing spectral correction and regularization techniques, termed SR-QDA. The regularization parameters in our method are selected by maximizing the Fisher-discriminant ratio. We compare SR-QDA with QDA, regularized quadratic discriminant analysis (R-QDA), and several other competitors. The results indicate that SR-QDA performs exceptionally well, especially in moderate and high-dimensional situations. Empirical experiments across diverse datasets further support this conclusion.

cs.LG↗

arXiv2024

Simultaneous test of the mean vectors and covariance matrices for high-dimensional data using RMT

In this paper, we propose a new modified likelihood ratio test (LRT) for simultaneously testing mean vectors and covariance matrices of two-sample populations in high-dimensional settings. By employing tools from Random Matrix Theory (RMT), we derive the limiting null distribution of the modified LRT for generally distributed populations. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the modified LRT exhibits favorable properties in terms of both size and power.

stat.AP↗

arXiv2024

Spectrally-Corrected and Regularized Linear Discriminant Analysis for Spiked Covariance Model

This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized discriminant analysis. With the support of a large-dimensional random matrix analysis framework, it is proved that SRLDA has a linear classification global optimal solution under the spiked model assumption. According to simulation data analysis, the SRLDA classifier performs better than RLDA and ILDA and is closer to the theoretical classifier. Experiments on different data sets show that the SRLDA algorithm performs better in classification and dimensionality reduction than currently used tools.

stat.ML↗

arXiv2024

Revised BDS Test

In this paper, we focus on the BDS test, which is a nonparametric test of independence. Specifically, the null hypothesis $H_{0}$ of it is that $\{u_{t}\}$ is i.i.d. (independent and identically distributed), where $\{u_{t}\}$ is a random sequence. The BDS test is widely used in economics and finance, but it has a weakness that cannot be ignored: over-rejecting $H_{0}$ even if the length $T$ of $\{u_{t}\}$ is as large as $(100,2000)$. To improve the over-rejection problem of BDS test, considering that the correlation integral is the foundation of BDS test, we not only accurately describe the expectation of the correlation integral under $H_{0}$, but also calculate all terms of the asymptotic variance of the correlation integral whose order is $O(T^{-1})$ and $O(T^{-2})$, which is essential to improve the finite sample performance of BDS test. Based on this, we propose a revised BDS (RBDS) test and prove its asymptotic normality under $H_{0}$. The RBDS test not only inherits all the advantages of the BDS test, but also effectively corrects the over-rejection problem of the BDS test, which can be fully confirmed by the simulation results we presented. Moreover, based on the simulation results, we find that similar to BDS test, RBDS test would also be affected by the parameter estimations of the ARCH-type model, resulting in size distortion, but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the model. Besides, through some actual datasets that have been demonstrated to fit well with ARCH-type models, we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem, and the results reflect that, under the same condition, the performance of the RBDS test is more encouraging.

math.ST↗