Tuning Parameter Estimation in Penalized Least Squares Methodology

E. Androulakis; C Koukouvinos; Kalliopi Mylona

doi:10.1080/03610918.2011.575507

Tuning Parameter Estimation in Penalized Least Squares Methodology

E. Androulakis, C Koukouvinos, Kalliopi Mylona

National Technical University of Athens

Research output: Contribution to journal › Article › peer-review

Abstract

The efficiency of the penalized methods (Fan and Li, 2001) depends strongly on a tuning parameter due to the fact that it controls the extent of penalization. Therefore, it is important to select it appropriately. In general, tuning parameters are chosen by data-driven approaches, such as the commonly used generalized cross validation. In this article, we propose an alternative method for the derivation of the tuning parameter selector in penalized least squares framework, which can lead to an ameliorated estimate. Simulation studies are presented to support theoretical findings and a comparison of the Type I and Type II error rates, considering the L1, the hard thresholding and the Smoothly Clipped Absolute Deviation penalty functions, is performed. The results are given in tables and discussion follows.

Original language	English
Pages (from-to)	1444–1457
Journal	Communications In Statistics-Simulation And Computation
Volume	40
DOIs	https://doi.org/10.1080/03610918.2011.575507
Publication status	Published - 1 Jun 2011

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10.1080/03610918.2011.575507

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title = "Tuning Parameter Estimation in Penalized Least Squares Methodology",

abstract = "The efficiency of the penalized methods (Fan and Li, 2001) depends strongly on a tuning parameter due to the fact that it controls the extent of penalization. Therefore, it is important to select it appropriately. In general, tuning parameters are chosen by data-driven approaches, such as the commonly used generalized cross validation. In this article, we propose an alternative method for the derivation of the tuning parameter selector in penalized least squares framework, which can lead to an ameliorated estimate. Simulation studies are presented to support theoretical findings and a comparison of the Type I and Type II error rates, considering the L1, the hard thresholding and the Smoothly Clipped Absolute Deviation penalty functions, is performed. The results are given in tables and discussion follows.",

author = "E. Androulakis and C Koukouvinos and Kalliopi Mylona",

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AU - Androulakis, E.

AU - Koukouvinos, C

AU - Mylona, Kalliopi

PY - 2011/6/1

Y1 - 2011/6/1

N2 - The efficiency of the penalized methods (Fan and Li, 2001) depends strongly on a tuning parameter due to the fact that it controls the extent of penalization. Therefore, it is important to select it appropriately. In general, tuning parameters are chosen by data-driven approaches, such as the commonly used generalized cross validation. In this article, we propose an alternative method for the derivation of the tuning parameter selector in penalized least squares framework, which can lead to an ameliorated estimate. Simulation studies are presented to support theoretical findings and a comparison of the Type I and Type II error rates, considering the L1, the hard thresholding and the Smoothly Clipped Absolute Deviation penalty functions, is performed. The results are given in tables and discussion follows.

AB - The efficiency of the penalized methods (Fan and Li, 2001) depends strongly on a tuning parameter due to the fact that it controls the extent of penalization. Therefore, it is important to select it appropriately. In general, tuning parameters are chosen by data-driven approaches, such as the commonly used generalized cross validation. In this article, we propose an alternative method for the derivation of the tuning parameter selector in penalized least squares framework, which can lead to an ameliorated estimate. Simulation studies are presented to support theoretical findings and a comparison of the Type I and Type II error rates, considering the L1, the hard thresholding and the Smoothly Clipped Absolute Deviation penalty functions, is performed. The results are given in tables and discussion follows.

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DO - 10.1080/03610918.2011.575507

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SP - 1444

EP - 1457

JO - Communications In Statistics-Simulation And Computation

JF - Communications In Statistics-Simulation And Computation

ER -

Tuning Parameter Estimation in Penalized Least Squares Methodology

Abstract

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