Kernel Ridge-Type Shrinkage Estimators in Partially Linear Regression Models with Correlated Errors

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2025-06

Department

Department of Computer Science

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Mcode

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Language

en

Pages

33

Series

Mathematics, Volume 13, issue 12, pp. 1-33

Abstract

Partially linear time series models often suffer from multicollinearity among regressors and autocorrelated errors, both of which can inflate estimation risk. This study introduces a generalized ridge-type kernel (GRTK) framework that combines kernel smoothing with ridge shrinkage and augments it through ordinary and positive-part Stein adjustments. Closed-form expressions and large-sample properties are established, and data-driven criteria—including GCV, AICc, BIC, and RECP—are used to tune the bandwidth and shrinkage penalties. Monte-Carlo simulations indicate that the proposed procedures usually reduce risk relative to existing semiparametric alternatives, particularly when the predictors are strongly correlated and the error process is dependent. An empirical study of US airline-delay data further demonstrates that GRTK produces a stable, interpretable fit, captures a nonlinear air-time effect overlooked by conventional approaches, and leaves only a modest residual autocorrelation. By tackling multicollinearity and autocorrelation within a single, flexible estimator, the GRTK family offers practitioners a practical avenue for more reliable inference in partially linear time series settings.

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Publisher Copyright: © 2025 by the authors.

Keywords

multicollinearity, parameter selection, partially linear models, ridge-type kernel smoother, shrinkage estimation

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DOI

10.3390/math13121959

Citation

Ahmed, S E, Yilmaz, E & Aydın, D 2025, 'Kernel Ridge-Type Shrinkage Estimators in Partially Linear Regression Models with Correlated Errors', Mathematics, vol. 13, no. 12, 1959, pp. 1-33. https://doi.org/10.3390/math13121959

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https://urn.fi/URN:NBN:fi:aalto-202508045741

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[article-cris] Perustieteiden korkeakoulu / SCI