arXiv subjects

Yanyan Ouyang

Publications and source records attributed to Yanyan Ouyang.

2 recordsLinked to original sources

arXiv2026

Random Projection Tests via Cauchy Combination for Two-Sample Mean

High-dimensional two-sample mean testing is challenging when the dimension exceeds the sample size. The random projection method proposed by Lopes et al. (2011) addresses this difficulty by mapping the data to a lower dimension space where Hotelling's $T^2$ statistic can be applied, while retaining useful covariance information and gaining power when the variables exhibit non-negligible covariance structure. However, single projection tests may be sensitive to the realized projection matrix, whereas existing multiple projection procedures often rely on resampling or simulation for calibration, with limited theoretical understanding. Moreover, projection-based Hotelling tests may be less sensitive to sparse mean differences. To address these limitations, we propose a Cauchy-combined random projection test (CRPT), which applies Hotelling's $T^2$ test after multiple independent random projections and combines the projected $p$-values through the Cauchy transformation. The proposed method retains the ability of random projection methods to incorporate covariance information while reducing reliance on any single projection. Under the Gaussian assumption, we establish the null tail behavior of the proposed statistic and further investigate its asymptotic power under suitable alternatives. To improve sensitivity to sparse alternatives, we further develop a power-enhanced version of CRPT. Simulation studies and real data analysis are conducted to examine the performance and practical applicability of the proposed procedures.

stat.ME↗

arXiv2024

Effective Positive Cauchy Combination Test

In the field of multiple hypothesis testing, combining p-values represents a fundamental statistical method. The Cauchy combination test (CCT) (Liu and Xie, 2020) excels among numerous methods for combining p-values with powerful and computationally efficient performance. However, large p-values may diminish the significance of testing, even extremely small p-values exist. We propose a novel approach named the positive Cauchy combination test (PCCT) to surmount this flaw. Building on the relationship between the PCCT and CCT methods, we obtain critical values by applying the Cauchy distribution to the PCCT statistic. We find, however, that the PCCT tends to be effective only when the significance level is substantially small or the test statistics are strongly correlated. Otherwise, it becomes challenging to control type I errors, a problem that also pertains to the CCT. Thanks to the theories of stable distributions and the generalized central limit theorem, we have demonstrated critical values under weak dependence, which effectively controls type I errors for any given significance level. For more general scenarios, we correct the test statistic using the generalized mean method, which can control the size under any dependence structure and cannot be further optimized. Our method exhibits excellent performance, as demonstrated through comprehensive simulation studies. We further validate the effectiveness of our proposed method by applying it to a genetic dataset.

stat.ME↗