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

Syed Ejaz Ahmed, Ersin Yilmaz () and Dursun Aydın
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Syed Ejaz Ahmed: Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A, Canada
Ersin Yilmaz: Department of Computer Science, Aalto University, Konemiehentie 2, 02150 Espoo, Finland
Dursun Aydın: Department of Statistics, Faculty of Science, Mugla Sitki Kocman University, Mugla 4800, Turkey

Mathematics, 2025, vol. 13, issue 12, 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.

Keywords: shrinkage estimation; partially linear models; multicollinearity; ridge-type kernel smoother; parameter selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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