Power-Dominance in Estimation Theory: A Third Pathological Axis
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915505986600960 |
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| author | Bulusu, Sri Satish Krishna Chaitanya Sillanpää, Mikko |
| author_facet | Bulusu, Sri Satish Krishna Chaitanya Sillanpää, Mikko |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12691 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power-Dominance in Estimation Theory: A Third Pathological Axis Bulusu, Sri Satish Krishna Chaitanya Sillanpää, Mikko Methodology Signal Processing Statistics Theory Machine Learning 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. |
| title | Power-Dominance in Estimation Theory: A Third Pathological Axis |
| topic | Methodology Signal Processing Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2509.12691 |