What does this research mean for the field?

Under weak-dependence noise, the Switching Degree estimator remains √n-asymptotically normal but requires a direction-dependent long-run variance correction to prevent severe under-coverage in confidence intervals. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To extend statistical inference for the Switching Degree estimator from independent and identically distributed noise to weakly dependent settings under alpha-mixing noise.

September 3, 2026Open Access

A General Asymptotic Normality Theorem for Switching Degree Inference under Weak Dependence — Direction-Dependent Long-Run Variance Correction, Moving Block Bootstrap Consistency, and Preservation of Structural Invariance

View Full Paper

Ask AI

Bookmark

Authors

STShuiping Tang

Discussion

Member takes

Implication

Theoretical analysis establishes asymptotic normality for switching degree inference under alpha-mixing noise, revealing that variance corrections prevent severe undercoverage.

Key Points

To extend statistical inference for the Switching Degree estimator from independent and identically distributed noise to weakly dependent settings under alpha-mixing noise.
Derived the asymptotic distribution and variance formula of the Switching Degree estimator under alpha-mixing noise conditions.
Formulated conditions for moving block bootstrap consistency and assessed structural invariance preservation under invertible isometries.
Evaluated the finite-sample performance of uncorrected, long-run variance corrected, and heteroskedasticity and autocorrelation consistent standard errors via numerical simulations.
The Switching Degree estimator maintains root-n asymptotic normality with an asymptotic variance determined by both instantaneous and long-run noise variance, which simplifies to the independent case when mean covariates or their projections vanish.
Structural invariance of the Switching Degree under invertible Sigma-isometries holds independently of noise independence assumptions.
Numerical simulations showed standard confidence intervals ignoring weak dependence suffered severe undercoverage dropping to 73%, whereas corrected theoretical intervals improved coverage to between 0.865 and 0.925.

Cite This Study

Shuiping Tang (2026) studied this question.

synapsesocial.com/papers/6a993592636c6408cfa7ddce https://doi.org/10.5281/zenodo.22219575

View Full Paper

Ask AI

Bookmark

Implication

Theoretical analysis establishes asymptotic normality for switching degree inference under alpha-mixing noise, revealing that variance corrections prevent severe undercoverage.

A General Asymptotic Normality Theorem for Switching Degree Inference under Weak Dependence — Direction-Dependent Long-Run Variance Correction, Moving Block Bootstrap Consistency, and Preservation of Structural Invariance

Discussion

Member takes

Implication

Key Points

Cite This Study

A General Asymptotic Normality Theorem for Switching Degree Inference under Weak Dependence — Direction-Dependent Long-Run Variance Correction, Moving Block Bootstrap Consistency, and Preservation of Structural Invariance

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider