{"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/empirical-bias-reducing-adjustments-to","title":"Empirical bias-reducing adjustments to estimating functions","arxiv_id":"2001.03786","date":"2020-01-11","proceeding":null,"authors":["Ioannis Kosmidis","Nicola Lunardon"],"abstract":"We develop a novel and general framework for reduced-bias $M$-estimation from asymptotically unbiased estimating functions. The framework relies on an empirical approximation of the bias by a function of derivatives of estimating function contributions. Reduced-bias $M$-estimation operates either implicitly, by solving empirically-adjusted estimating equations, or explicitly, by subtracting the estimated bias from the original $M$-estimates, and applies to models that are partially- or fully-specified, with either likelihoods or other surrogate objectives. Automatic differentiation can be used to abstract away the only algebra required to implement reduced-bias $M$-estimation. As a result, the bias reduction methods we introduce have markedly broader applicability with more straightforward implementation and less algebraic or computational effort than other established bias-reduction methods that require resampling or evaluation of expectations of products of log-likelihood derivatives. If $M$-estimation is by maximizing an objective, then there always exists a bias-reducing penalized objective. That penalized objective relates closely to information criteria for model selection, and can be further enhanced with plug-in penalties to deliver reduced-bias $M$-estimates with extra properties, like finiteness in models for categorical data. The reduced-bias $M$-estimators have the same asymptotic distribution as the original $M$-estimators, and, hence, standard procedures for inference and model selection apply unaltered with the improved estimates. We demonstrate and assess the properties of reduced-bias $M$-estimation in well-used, prominent modelling settings of varying complexity.","url_abs":"https://arxiv.org/abs/2001.03786v4","url_pdf":"https://arxiv.org/pdf/2001.03786v4.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"empirical-bias-reducing-adjustments-to","repo_url":"https://github.com/ikosmidis/MEstimation.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}