What does this research mean for the field?

Generalizing the Switching Degree to function spaces via a dual-objective design—combining L² influence functions in series estimation and RKHS spectral weighting—provides a valid effect size measure for nonlinear regime switching that achieves nominal coverage in finite samples with known boundaries. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To generalize the switching degree effect size from linear parameter spaces to function spaces for measuring nonlinear regime switching.

September 2, 2026Open Access

The Switching Degree for Nonlinear Regime Switching — L² Influence Functions in a Series Estimation Framework, the Spectral Weighting Family, and Finite-Sample Inference

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Authors

STShuiping Tang

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Implication

Methodological study demonstrates finite-sample inference for nonlinear switching degrees in function spaces, indicating a robust framework for structural breaks.

Key Points

To generalize the switching degree effect size from linear parameter spaces to function spaces for measuring nonlinear regime switching.
Targeted the L² switching degree using series estimation on Fourier and polynomial bases to derive an explicit influence function without requiring reproducing kernel Hilbert space (RKHS) inverse operators.
Unified L² and RKHS switching metrics through a spectral weighting family and derived an orthogonal projection algorithm for linear-nonlinear decomposition.
Evaluated finite-sample coverage, bias, and root-mean-square error (RMSE) under known versus unknown boundaries and under heteroskedasticity.
The influence-function debiased estimator achieved nominal coverage of 95.4% to 96.8% with absolute bias below 0.003 and monotonically decreasing RMSE when the truncation bias grew slower than n^(-1/2).
Confidence coverage dropped to approximately 71.4% when regime boundaries were unknown, highlighting the need for finite-sample post-selection corrections.
White's robust variance improved coverage under heteroskedasticity from 63.2% to 76.4%, though remaining below the nominal level.

Cite This Study

Shuiping Tang (2026) studied this question.

synapsesocial.com/papers/6a97e2f6c562ede874ec773d https://doi.org/10.5281/zenodo.22201822

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Implication

Methodological study demonstrates finite-sample inference for nonlinear switching degrees in function spaces, indicating a robust framework for structural breaks.

The Switching Degree for Nonlinear Regime Switching — L² Influence Functions in a Series Estimation Framework, the Spectral Weighting Family, and Finite-Sample Inference

Discussion

Member takes

Implication

Key Points

Cite This Study

The Switching Degree for Nonlinear Regime Switching — L² Influence Functions in a Series Estimation Framework, the Spectral Weighting Family, and Finite-Sample Inference

Discussion

Member takes

Implication

Key Points

Cite This Study

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