What does this research mean for the field?

In the fixed-breakpoint model, the plug-in estimator of the switching degree with an unknown boundary is asymptotically equivalent to the known-boundary estimator at the √n scale. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish whether estimating an unknown regime boundary alters the asymptotic distribution of switching degree estimators in fixed-breakpoint structural break models.

September 2, 2026Open Access

Asymptotic Equivalence of the Switching Degree with Unknown Boundary — √n-Inference Adaptivity in the Fixed-Breakpoint Model, Finite-Sample Correction Directions, and a Post-Selection Inference Framework

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STShuiping Tang

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Implication

Theoretical analysis demonstrates asymptotic equivalence between plug-in and known-boundary estimators in fixed-breakpoint models, indicating robust large-sample inference.

Key Points

To establish whether estimating an unknown regime boundary alters the asymptotic distribution of switching degree estimators in fixed-breakpoint structural break models.
Conducted mathematical proofs under regularity assumptions A1–A7 for a fixed-breakpoint model with a non-zero parameter shift vector.
Evaluated sample misclassification rates and their downstream influence on regime-specific regression coefficient estimators.
Formulated theoretical finite-sample correction proposals, including conditional bias expansion and a fixed-design residual bootstrap framework.
Proved the asymptotic equivalence theorem showing √n (Ŝ_plug − Ŝ_known) = o_p(1), confirming √n (Ŝ_plug − S) converges in distribution to N(0, V₀) identically to the known-boundary estimator.
Demonstrated that boundary estimator n-consistency confines misclassified observations to O_p(1), restricting their coefficient impact to O_p(n⁻¹) and rendering selection effects invisible at the √n scale.
Proposed finite-sample post-selection bias expansions and asymmetric bootstrap quantile intervals to address finite-sample distortions.

Cite This Study

Shuiping Tang (2026) studied this question.

synapsesocial.com/papers/6a97e2c5c562ede874ec71e8 https://doi.org/10.5281/zenodo.22204349

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Implication

Theoretical analysis demonstrates asymptotic equivalence between plug-in and known-boundary estimators in fixed-breakpoint models, indicating robust large-sample inference.

Asymptotic Equivalence of the Switching Degree with Unknown Boundary — √n-Inference Adaptivity in the Fixed-Breakpoint Model, Finite-Sample Correction Directions, and a Post-Selection Inference Framework

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Cite This Study

Asymptotic Equivalence of the Switching Degree with Unknown Boundary — √n-Inference Adaptivity in the Fixed-Breakpoint Model, Finite-Sample Correction Directions, and a Post-Selection Inference Framework

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