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August 19, 2026Stochastic Models

The asymptotics for the estimators in a semiparametric regression model under infinite r -th moments

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Authors

YWYan WangASAiting Shen

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Overview

Theoretical analysis demonstrates weak consistency for semiparametric regression estimators under infinite moments, suggesting improved reliability when error distributions have heavy tails.

Key Points

  • To establish the asymptotic behavior and weak consistency of both parametric and nonparametric component estimators in semiparametric regression models under infinite r-th moments (1 < r < 2).
  • Analyzed semiparametric regression models with independent zero-mean errors stochastically dominated by a random variable with a slowly varying truncated moment function.
  • Derived mathematical proofs of weak consistency under infinite moment conditions (1 < r < 2).
  • Validated theoretical findings through numerical simulation studies and real-world data analysis.
  • Established weak consistency for both parametric and nonparametric component estimators under infinite r-th moments (1 < r < 2).
  • Generalized existing asymptotic properties from identically distributed random errors with finite moments to stochastically dominated errors with infinite moments.

Cite This Study

Wang et al. (2026) studied this question.

synapsesocial.com/papers/6a858aaf03308d306e2d7f7ehttps://doi.org/10.1080/15326349.2026.2714787
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