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Brown Bag Lunch Series
July 20 @ 12:30 pm - 1:30 pm PDT
Presenter: Mohamed Megheib
Title: Bandwidth Selection Methods for Nonparametric Regression with Spatially Correlated Data
Abstract: In nonparametric regression estimation, a critical and inevitable step is to choose the smoothing parameters (bandwidth) to control the smoothness of the curve estimate. In the presence of spatially correlated errors, the traditional data-driven bandwidth selection methods, such as cross-validation and generalized cross-validation, do not work well for providing efficient bandwidth values. Moreover, the existing methods are based on estimation of correlation structure. As errors are unobservable, estimation of correlation is considered as a big challenge. We study bandwidth selection methods for local linear regression (LLR) in the presence of correlated errors. We derive the Weighted Mean Average Square Errors (WMASE) and use it along with Bias-Correlated Generalized Cross-Validation (GCV) as bandwidth selection criterion.
Due to its good properties, the composite likelihood (CL) is used to estimate the correlation. This is done in two ways: by minimizing the Weighted Mean Average Square Errors (WMASE) and by using the Bias-Correlated Generalized Cross-Validation (GCV) criterion. The results show that the composite likelihood provides better estimates than maximum likelihood (ML) in the sense of producing more reasonable bandwidth. Also, our methods appear reasonably robust for misspecification of correlation models. Moreover, the proposed methods work much better than ignoring the correlation and applying tradition methods.