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The ROPE framework for model selection in linear regression

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posted on 2022-11-18, 01:03 authored by Ibrahim Joudah

Many methods for model selection fall under the “Loss + Penalty” approach, where the “Loss” prizes the model for fitting the data well and the “Penalty” penalizes the model for its complexity. One method in particular (the Fence method) uses a data adaptive bootstrapping algorithm, the Adaptive Fence (AF), to select the penalty. The goal of the AF algorithm is to estimate the optimal penalty, i.e., the penalty that maximize the probability of selecting the true data generating model, which is a common desired objective for model selection. We show how the AF approach for estimating the optimal penalty can be improved and propose a new algorithm that can provide a better estimate, which we coin the Resampling-based Optimal Penalty Estimate (ROPE) algorithm. We show how to implement both algorithms to select the penalty multiplier in the Generalized Information Criteria (GIC) for model selection in linear regression. Then, we carry out a simulation study to compare the two algorithms. The results of the study indicate that the ROPE algorithm outperforms the AF algorithm in our simulation settings.

History

Table of Contents

1. Introduction -- 2. Review -- 3. Methods and Algorithms -- 4. Simulation Study -- References

Notes

A thesis submitted to Macquarie University for the degree of Master of Research

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

Thesis (MRes), Macquarie University, Faculty of Science and Engineering, 2022

Department, Centre or School

School of Mathematical and Physical Sciences

Year of Award

2022

Principal Supervisor

Samuel Muller

Additional Supervisor 1

Houying Zhu

Rights

Copyright: Ibrahim Joudah Copyright disclaimer: https://www.mq.edu.au/copyright-disclaimer

Language

English

Extent

62 pages

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