What does this research mean for the field?

In structural break detection, the standardized limits of Chow F, Wald, and LR statistics share a unified shape function and attain their unique global maximum precisely at the true regime boundary. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish a unified mathematical invariant theory for regression difference statistics used to identify true regime boundaries in structural break detection models.

September 2, 2026Open Access

The Global Maximum Point Invariance Theorem: A Statistical Invariant Theory of Structural Break Detection — Unified Shape Function, Standardized Limits, and Multi-Regime Generalization

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STShuiping Tang

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Implication

Theoretical study proves global maximum invariance for regression difference statistics in switching models, indicating guaranteed exact boundary recovery during structural break detection.

Key Points

To establish a unified mathematical invariant theory for regression difference statistics used to identify true regime boundaries in structural break detection models.
Derived analytical limits as sample size approaches infinity (n → ∞) for Chow F, Wald, and likelihood ratio statistics within a two-regime linear switching model.
Formulated non-asymptotic shrinkage bounds and multi-regime optimality proofs using convex combination geometry, statistical algebra, and the Bayesian information criterion.
Tested slow-variation robustness analytically and numerically verified the theorems using the Onsager–Yang exact solution of the 2D Ising model.
Proved that standardized limits of Chow F/n, Wald/n, and LR/n uniquely reach their global maximum at the true regime boundary via a common monotone shape function h(τ).
Established that estimated coefficients at misallocated boundaries converge to mixed parameters at rate n^(−1/2), suppressing false statistic peaks in finite samples with high probability.
Demonstrated exact boundary localization in the 2D Ising model at critical temperature T_c = 2.269185 with perfect rank monotonicity (ρ = 1.0000).

Cite This Study

Shuiping Tang (2026) studied this question.

synapsesocial.com/papers/6a97e249c562ede874ec6545 https://doi.org/10.5281/zenodo.22201405

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Implication

Theoretical study proves global maximum invariance for regression difference statistics in switching models, indicating guaranteed exact boundary recovery during structural break detection.

The Global Maximum Point Invariance Theorem: A Statistical Invariant Theory of Structural Break Detection — Unified Shape Function, Standardized Limits, and Multi-Regime Generalization

Discussion

Member takes

Implication

Key Points

Cite This Study

The Global Maximum Point Invariance Theorem: A Statistical Invariant Theory of Structural Break Detection — Unified Shape Function, Standardized Limits, and Multi-Regime Generalization

Discussion

Member takes

Implication

Key Points

Cite This Study

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