What does this research mean for the field?

The proposed one-sided kernel locally weighted unified shape function eliminates the pseudo-peak phenomenon of global splitting by establishing a one-to-one correspondence between its local maxima and true regime boundaries. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To resolve the convex-combination pseudo-peak problem in multi-regime structural break detection by establishing a localized shape function framework that guarantees a one-to-one correspondence with true boundaries.

September 14, 2026Open Access

Locally Weighted Unified Shape Function and the One-to-One Correspondence with Regime Boundaries: Multi-Regime Local Peak Correspondence, Population Limit Geometry, and the Pseudo-Peak Phenomenon of Global Splitting

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To resolve the convex-combination pseudo-peak problem in multi-regime structural break detection by establishing a localized shape function framework that guarantees a one-to-one correspondence with true boundaries.
Constructed a one-sided kernel locally weighted unified shape function by performing separate locally weighted least squares across left and right windows of candidate thresholds and calculating the squared Mahalanobis norm of coefficient differences.
Analyzed the theoretical geometry and asymptotic properties under a k-regime linear switching model with bandwidth conditions b_n → 0 and n b_n / log n → ∞.
Verified finite-sample efficacy using permutation testing and numerical simulations on a multi-regime counterexample exhibiting global pseudo-peaks.
Proved that local maxima of the localized shape function correspond pointwise in probability to true regime boundaries with an estimation error of O_p(b_n).
Demonstrated an explicit three-regime counterexample where the global estimator produced an inter-boundary pseudo-peak of h(0.5) = 46.23 exceeding the weakest true boundary peak of h(τ₁*) = 30.71, whereas the local method achieved a 100% correct detection rate.
Showed that under the null hypothesis, the supremum of the test statistic satisfies O_p(log n / (n b_n)) and the permutation test strictly controls the false positive rate.

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Implication

Theoretical analysis reveals that locally weighted shape functions eliminate pseudo-peaks in multi-regime switching models, indicating reliable identification of true structural boundaries.

Cite This Study

Shuiping Tang (2026) studied this question.

synapsesocial.com/papers/6aa7b3770926e14a848b26e2 https://doi.org/10.5281/zenodo.22700677

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Implication

Theoretical analysis reveals that locally weighted shape functions eliminate pseudo-peaks in multi-regime switching models, indicating reliable identification of true structural boundaries.

Locally Weighted Unified Shape Function and the One-to-One Correspondence with Regime Boundaries: Multi-Regime Local Peak Correspondence, Population Limit Geometry, and the Pseudo-Peak Phenomenon of Global Splitting

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Discussion

Implication

Cite This Study

Locally Weighted Unified Shape Function and the One-to-One Correspondence with Regime Boundaries: Multi-Regime Local Peak Correspondence, Population Limit Geometry, and the Pseudo-Peak Phenomenon of Global Splitting

Key Points

Discussion

Implication

Cite This Study

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