{"ID":2870192,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.12691","arxiv_id":"2509.12691","title":"Power-Dominance in Estimation Theory: A Third Pathological Axis","abstract":"This paper introduces a novel framework for estimation theory by introducing a second-order diagnostic for estimator design. While classical analysis focuses on the bias-variance trade-off, we present a more foundational constraint. This result is model-agnostic, domain-agnostic, and is valid for both parametric and non-parametric problems, Bayesian and frequentist frameworks. We propose to classify the estimators into three primary power regimes. We theoretically establish that any estimator operating in the `power-dominant regime' incurs an unavoidable mean-squared error penalty, making it structurally prone to sub-optimal performance. We propose a `safe-zone law' and make this diagnostic intuitive through two safe-zone maps. One map is a geometric visualization analogous to a receiver operating characteristic curve for estimators, and the other map shows that the safe-zone corresponds to a bounded optimization problem, while the forbidden `power-dominant zone' represents an unbounded optimization landscape. This framework reframes estimator design as a path optimization problem, providing new theoretical underpinnings for regularization and inspiring novel design philosophies.","short_abstract":"This paper introduces a novel framework for estimation theory by introducing a second-order diagnostic for estimator design. While classical analysis focuses on the bias-variance trade-off, we present a more foundational constraint. This result is model-agnostic, domain-agnostic, and is valid for both parametric and no...","url_abs":"https://arxiv.org/abs/2509.12691","url_pdf":"https://arxiv.org/pdf/2509.12691v2","authors":"[\"Sri Satish Krishna Chaitanya Bulusu\",\"Mikko Sillanpää\"]","published":"2025-09-16T05:33:21Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"eess.SP\",\"math.ST\",\"stat.ML\"]","methods":"[]","has_code":false}