Macquarie University
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Local polynomial M-estimation in random design regression with dependent errors

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posted on 2022-03-29, 00:46 authored by Yixuan Liu
The random design nonparametric regression model with short-range dependent and long-range dependent errors is investigated. The asymptotic behaviour of the robust local polynomial M-estimator is investigated under two conditions. Asymptotic results are established by decomposing the local polynomial estimator into two terms: a martingale term and a conditional expectation term. It is found that the local polynomial M-estimator is asymptotically normal when errors are short-range dependent. When the errors are long-range dependent, a more complex behaviour is observed that depends on the size of the bandwidth. If the bandwidth is small enough, the long-range dependent scenario is similar to the the short-range dependent case. If the bandwidth is relatively large the asymptotic result is more intricate and the long-range dependent variables dominate. Moreover, the optimal bandwidth in the case of short-range dependence is determined.


Table of Contents

1. Introduction -- 2. Notations and assumptions -- 3. Results -- 4. Conclusion -- 5. Proofs.


Theoretical thesis. Bibliography: pages 51-53

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics and Statistics

Department, Centre or School

Department of Mathematics and Statistics

Year of Award


Principal Supervisor

Justin Wishart


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1 online resource (53 pages)

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