{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sequential-quantiles-via-hermite-series","title":"Sequential Quantiles via Hermite Series Density Estimation","arxiv_id":"1507.05073","date":"2015-07-17","proceeding":null,"authors":["Michael Stephanou","Melvin Varughese","Iain Macdonald"],"abstract":"Sequential quantile estimation refers to incorporating observations into\nquantile estimates in an incremental fashion thus furnishing an online estimate\nof one or more quantiles at any given point in time. Sequential quantile\nestimation is also known as online quantile estimation. This area is relevant\nto the analysis of data streams and to the one-pass analysis of massive data\nsets. Applications include network traffic and latency analysis, real time\nfraud detection and high frequency trading. We introduce new techniques for\nonline quantile estimation based on Hermite series estimators in the settings\nof static quantile estimation and dynamic quantile estimation. In the static\nquantile estimation setting we apply the existing Gauss-Hermite expansion in a\nnovel manner. In particular, we exploit the fact that Gauss-Hermite\ncoefficients can be updated in a sequential manner. To treat dynamic quantile\nestimation we introduce a novel expansion with an exponentially weighted\nestimator for the Gauss-Hermite coefficients which we term the Exponentially\nWeighted Gauss-Hermite (EWGH) expansion. These algorithms go beyond existing\nsequential quantile estimation algorithms in that they allow arbitrary\nquantiles (as opposed to pre-specified quantiles) to be estimated at any point\nin time. In doing so we provide a solution to online distribution function and\nonline quantile function estimation on data streams. In particular we derive an\nanalytical expression for the CDF and prove consistency results for the CDF\nunder certain conditions. In addition we analyse the associated quantile\nestimator. Simulation studies and tests on real data reveal the Gauss-Hermite\nbased algorithms to be competitive with a leading existing algorithm.","url_abs":"http://arxiv.org/abs/1507.05073v2","url_pdf":"http://arxiv.org/pdf/1507.05073v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sequential-quantiles-via-hermite-series","repo_url":"https://github.com/MikeJaredS/hermiter","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"data-summarization","task_name":"Data Summarization"},{"task_slug":"sequential-distribution-function-estimation","task_name":"Sequential Distribution Function Estimation"},{"task_slug":"sequential-quantile-estimation","task_name":"Sequential Quantile Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}