What does this research mean for the field?

The Switching Degree provides a uniquely axiomatized effect size for quantifying regime switches in structural break detection, though its estimation under unknown boundaries exhibits a systematic negative bias that naive bootstrap methods cannot correct. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish an axiomatic foundation, asymptotic inference theory, power analysis, and decomposition framework for a standardized effect size measuring the magnitude of structural regime shifts.

September 2, 2026Open Access

Switching Degree: An Axiomatic Effect Size for Structural Break Detection — Axiomatic Foundation, Inference Theory, Power Analysis, and Switching Coupling Decomposition of Regime-Switch Metrics

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STShuiping Tang

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Implication

Methodological study reveals properties of the Switching Degree in structural break detection, highlighting systematic post-selection bias under unknown boundaries.

Key Points

To establish an axiomatic foundation, asymptotic inference theory, power analysis, and decomposition framework for a standardized effect size measuring the magnitude of structural regime shifts.
Defined local Switching Degree S via Mahalanobis norm ratio and global effect size S_eff standardized by noise, linking to Cohen's f².
Derived asymptotic distributions, non-asymptotic shrinkage bounds, heteroskedasticity corrections, and first-order bias expansions under known and unknown break boundaries.
Evaluated finite-sample inference and coverage using numerical simulations and a 2D Ising model calibrated to Onsager critical temperature.
Proved axiomatic uniqueness under norm axioms and derived asymptotic normality: √n(Ŝ − S) converges to N(0, σ² / [γ(1 − γ)‖θ_ref‖_Σ²]).
Demonstrated that boundary estimation error induces systematic underestimation with first-order bias Ŝ_plug − S = −ηS + o_p(n^(−1/2)), yielding empirical bias equal to ~81% of the standard error.
Showed residual bootstrap quantile intervals achieved only 86.5% coverage compared to the nominal 95% under unknown boundaries, indicating naive resampling cannot correct post-selection bias.

Cite This Study

Shuiping Tang (2026) studied this question.

synapsesocial.com/papers/6a97e2eac562ede874ec7582 https://doi.org/10.5281/zenodo.22201322

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Implication

Methodological study reveals properties of the Switching Degree in structural break detection, highlighting systematic post-selection bias under unknown boundaries.

Switching Degree: An Axiomatic Effect Size for Structural Break Detection — Axiomatic Foundation, Inference Theory, Power Analysis, and Switching Coupling Decomposition of Regime-Switch Metrics

Discussion

Member takes

Implication

Key Points

Cite This Study

Switching Degree: An Axiomatic Effect Size for Structural Break Detection — Axiomatic Foundation, Inference Theory, Power Analysis, and Switching Coupling Decomposition of Regime-Switch Metrics

Discussion

Member takes

Implication

Key Points

Cite This Study

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