In this paper, we derive a precise false alarm rate of the SUM-CUSUM scheme when monitoring high-dimensional data streams or large-scale local data streams in the modern asymptotic regime, where the dimensionality of data tends to infinity. Both high-level easy-to-understand arguments and rigorous proofs based on the localization Theorem from Yakir (2013) are provided. The result enables us to improve a hypothesized detection threshold of the SUM-CUSUM scheme made in Mei (Biometrika, 2010) to achieve the desired false alarm rate.

MOTIVATION: The rise in the number of genotyped ancient individuals provides an opportunity to estimate population admixture models for many populations. However, in models describing modern populations as mixtures of ancient ones, it is typically difficult to estimate the model mixing coefficients and to evaluate its fit to the data. RESULTS: We present LINADMIX, designed to tackle this problem by solving a constrained linear model when both the ancient and the modern genotypes are represented in a low-dimensional space. LINADMIX estimates the mixing coefficients and their standard errors, and computes a P-value for testing the model fit to the data. We quantified the performance of LINADMIX using an extensive set of simulated studies. We show that LINADMIX can accurately estimate admixture coefficients, and is robust to factors such as population size, genetic drift, proportion of missing data and various types of model misspecification. AVAILABILITY AND IMPLEMENTATION: LINADMIX is available as a python code at https://github.com/swidler/linadmix. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.