arXiv subjects

Tung-Lung Wu

Publications and source records attributed to Tung-Lung Wu.

4 recordsLinked to original sources

arXiv2026

Scan Statistics for Nonhomogeneous Poisson Processes with Extreme-Value Calibration and Application to CNV Detection

We develop a scan statistic method for detecting local clusters in a two-sample nonhomogeneous Poisson process (NHPP) framework, motivated by copy number variation (CNV) analysis in next-generation sequencing data. The control sample is used to construct an empirical time transformation, under which the transformed case sample is approximately uniform on [0,1] under the null hypothesis. The scan statistic is defined as the maximum number of transformed points within a moving window. We show that the scan statistic converges to a generalized extreme value (GEV) distribution with an extremal index that captures the dependence induced by overlapping windows. The GEV parameters and extremal index are estimated using maximum likelihood and exceedance clustering methods, providing an asymptotic calibration of the test. A permutation procedure is also developed to provide a nonparametric alternative. Simulation studies show that the permutation calibration maintains empirical Type I error close to the nominal level across the considered settings, and the GEV calibration is accurate for smaller windows. Both proposed procedures show competitive power compared with the continuous testing method under heterogeneous baseline intensities. An application to sequencing data illustrates the effectiveness of the proposed approach for detecting CNV regions.

stat.ME↗

arXiv2025

Distribution-Free Control Charts Based on Runs and Patterns

We propose distribution-free runs-based control charts for detecting location shifts. Using the fact that given the number of total successes, the outcomes of a sequence of Bernoulli trials are random permutations, we are able to control the conditional probability of a signal detected at current time given that there is not alarm before at a pre-determined level. This leads to a desired in-control average run length and data-dependent control limits. Two common runs statistics, the longest run statistic and the scan statitsic, are studied in detail and their exact conditional distributions given the number of total successes are obtained using the finite Markov chain imbedding technique. Numerical results are given to evaluate the performance of the proposed control charts.

stat.ME↗

arXiv2025

Phase I Distribution-Free Control Charts for Individual Observations Using Runs and Patterns

Phase I distribution-free runs- and patterns-type control charts are proposed for monitoring the unknown target value (or location parameter) for both continuous and discrete individual observations. Our approach maintains the nominal in-control signal probability at a prescribed level by employing the finite Markov chain imbedding technique combined with random permutation and conditioning arguments. To elucidate the methodology, we examine two popular runs- and patterns-type statistics: the number of success runs and the scan statistic. Numerical results indicate that the performance of our proposed control charts is comparable to that of existing Phase I nonparametric control charts for individual observations.

stat.AP↗

arXiv2015

Tests for High-Dimensional Covariance Matrices Using Random Matrix Projection

The classic likelihood ratio test for testing the equality of two covariance matrices breakdowns due to the singularity of the sample covariance matrices when the data dimension $p$ is larger than the sample size $n$. In this paper, we present a conceptually simple method using random projection to project the data onto the one-dimensional random subspace so that the conventional methods can be applied. Both one-sample and two-sample tests for high-dimensional covariance matrices are studied. Asymptotic results are established and numerical results are given to compare our method with state-of-the-art methods in the literature.

stat.ME↗