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DOI :10.26650/ijmath.2024.00020   IUP :10.26650/ijmath.2024.00020    Full Text (PDF)

A New Liu-Ratio Estimator For Linear Regression Models

İsmail Müfit Giresunlu, Kadri Ulaş Akay, Esra Ertan

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables. Although there are various methods for estimating parameters, the most popular is the Ordinary Least Squares (OLS) method. However, in the presence of multicollinearity and outliers, the OLS estimator may give inaccurate values and also misleading inference results. There are many modified biased robust estimators for the simultaneous occurrence of outliers and multicollinearity in the data. In this paper, a new estimator called the Liu-Ratio Estimator (LRE), which can be used as an alternative to the Least Squares Ratio (LSR) estimator and the Ridge Ratio estimator (RRE), is proposed to mitigate the effect of 𝑦-direction outliers and multicollinearity in the data. The performance of the proposed estimator is examined in two Monte Carlo simulation studies in the presence of multicollinearity and 𝑦-direction outliers. According to the simulation results, LRE is a strong alternative to LSR and RRE in the presence of multicollinearity and 𝑦-direction outliers in the data. 

Keywords: Least Squares Ratio Estimator, Liu Estimator, Multicollinearity, Ridge Estimator

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Citations

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APA

Giresunlu, İ.M., Akay, K.U., & Ertan, E. (2024). A New Liu-Ratio Estimator For Linear Regression Models. Istanbul Journal of Mathematics, 2(2), 95-108. https://doi.org/10.26650/ijmath.2024.00020


AMA

Giresunlu İ M, Akay K U, Ertan E. A New Liu-Ratio Estimator For Linear Regression Models. Istanbul Journal of Mathematics. 2024;2(2):95-108. https://doi.org/10.26650/ijmath.2024.00020


ABNT

Giresunlu, İ.M.; Akay, K.U.; Ertan, E. A New Liu-Ratio Estimator For Linear Regression Models. Istanbul Journal of Mathematics, [Publisher Location], v. 2, n. 2, p. 95-108, 2024.


Chicago: Author-Date Style

Giresunlu, İsmail Müfit, and Kadri Ulaş Akay and Esra Ertan. 2024. “A New Liu-Ratio Estimator For Linear Regression Models.” Istanbul Journal of Mathematics 2, no. 2: 95-108. https://doi.org/10.26650/ijmath.2024.00020


Chicago: Humanities Style

Giresunlu, İsmail Müfit, and Kadri Ulaş Akay and Esra Ertan. “A New Liu-Ratio Estimator For Linear Regression Models.” Istanbul Journal of Mathematics 2, no. 2 (Feb. 2025): 95-108. https://doi.org/10.26650/ijmath.2024.00020


Harvard: Australian Style

Giresunlu, İM & Akay, KU & Ertan, E 2024, 'A New Liu-Ratio Estimator For Linear Regression Models', Istanbul Journal of Mathematics, vol. 2, no. 2, pp. 95-108, viewed 5 Feb. 2025, https://doi.org/10.26650/ijmath.2024.00020


Harvard: Author-Date Style

Giresunlu, İ.M. and Akay, K.U. and Ertan, E. (2024) ‘A New Liu-Ratio Estimator For Linear Regression Models’, Istanbul Journal of Mathematics, 2(2), pp. 95-108. https://doi.org/10.26650/ijmath.2024.00020 (5 Feb. 2025).


MLA

Giresunlu, İsmail Müfit, and Kadri Ulaş Akay and Esra Ertan. “A New Liu-Ratio Estimator For Linear Regression Models.” Istanbul Journal of Mathematics, vol. 2, no. 2, 2024, pp. 95-108. [Database Container], https://doi.org/10.26650/ijmath.2024.00020


Vancouver

Giresunlu İM, Akay KU, Ertan E. A New Liu-Ratio Estimator For Linear Regression Models. Istanbul Journal of Mathematics [Internet]. 5 Feb. 2025 [cited 5 Feb. 2025];2(2):95-108. Available from: https://doi.org/10.26650/ijmath.2024.00020 doi: 10.26650/ijmath.2024.00020


ISNAD

Giresunlu, İsmailMüfit - Akay, KadriUlaş - Ertan, Esra. “A New Liu-Ratio Estimator For Linear Regression Models”. Istanbul Journal of Mathematics 2/2 (Feb. 2025): 95-108. https://doi.org/10.26650/ijmath.2024.00020



TIMELINE


Submitted17.09.2024
Accepted31.12.2024
Published Online31.12.2024

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