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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 75 Issue: 2

Robust Parameter Estimation in PLMs with Skewed and Heavy-tailed Error Distributions

Fatma Zehra Doğru(Giresun Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü)0000-0001-8220-2375
Olcay Arslan(ANKARA ÜNİVERSİTESİ, FEN FAKÜLTESİ, İSTATİSTİK BÖLÜMÜ, İSTATİSTİK TEORİSİ ANABİLİM DALI)0000-0002-7067-4997
Sayfa
—
Yayın Tarihi
2026-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The proposed method is validated using simulation experiments and applied to an empirical dataset to highlight its practical utility.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Partially linear models (PLMs) provide a flexible extension of classical linear models by incorporating parametric and nonparametric components, making them suitable for complex data structures often encountered in economics and biometrics.
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Temel Bulgular & Veri:Traditionally, these models assume normally distributed errors, an assumption that may not hold in many practical scenarios.
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Sonuç & Katkı:The proposed method is validated using simulation experiments and applied to an empirical dataset to highlight its practical utility.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:ECM algorithm · maximum likelihood estimation · PLM-SLN

Abstract

Partially linear models (PLMs) provide a flexible extension of classical linear models by incorporating parametric and nonparametric components, making them suitable for complex data structures often encountered in economics and biometrics. Traditionally, these models assume normally distributed errors, an assumption that may not hold in many practical scenarios. To address this, previous studies introduced the skew normal distribution in PLMs (PLM-SN) to account for asymmetry. However, such data sets may also exhibit heavy tails and skewness. To capture both characteristics, we propose a new approach: modeling the error structure using the skewed Laplace normal distribution (PLM-SLN), which maintains the same number of parameters as PLM-SN but better accommodates heavy-tailed behavior. An efficient estimation procedure using an expectation-conditional maximization (ECM) algorithm is developed to compute maximum likelihood estimates. The proposed method is validated using simulation experiments and applied to an empirical dataset to highlight its practical utility.

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Bu Makaleye Atıf Yap

Doğru, F. Z., Arslan, O. (2026). Robust Parameter Estimation in PLMs with Skewed and Heavy-tailed Error Distributions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 75 Issue: 2. https://doi.org/10.31801/cfsuasmas.1677165

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