2019/02/25 by Laura Jula Vanegas, Vanegas, Laura Jula, Merle Behr +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #62G08 #62G15 #62G30 #62G35 #90C39 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Gene expression and cancer classification #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1902.09321
openalex publication_date 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial independence. It is based on a multiscale statistic, which allows to control the (finite sample) probability for selecting the correct number of segments S at a given error level, which serves as a tuning parameter. For a proper choice of this parameter, this tends exponentially fast to the true S, as sample size increases. We further show that the location and size of segments are estimated at minimax optimal rate (compared to a Gaussian setting) up to a log-factor. Thereby, our approach leads to (asymptotically) uniform confidence bands for the entire quantile regression function in a fully nonparametric setup. The procedure is efficiently implemented using dynamic programming techniques with double heap structures, and software is provided. Simulations and data examples from genetic sequencing and ion channel recordings confirm the robustness of the proposed procedure, which at the same hand reliably detects changes in quantiles from arbitrary distributions with precise statistical guarantees.