New Parsimonious Multivariate Spatial Model: Spatial Envelope

Rekabdarkolaee, Hossein Moradi; Wang, Qin; Naji, Zahra; Fuentes, Montserrat

doi:10.48550/arxiv.1706.06703

Cited by 1 publication

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“…Li and Zhang (2017) and Ding and Cook (2018) developed envelope models for tensor and matrix regression problems. Spatial envelopes and envelopes for time series data were proposed and studied in Rekabdarkolaee et al (2017) and Wang and Ding (2018). For a comprehensive overview of envelope methods, see Cook (2018).…”

Section: Introductionmentioning

confidence: 99%

Enveloped Huber Regression

Zhou¹,

Cook²,

Zou³

2020

Preprint

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Huber regression (HR) is a popular robust alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope assumption that there exists some subspace of the predictors that has no association with the response, which is referred to as the immaterial part. More efficient estimation is achieved via the removal of the immaterial part.Different from the envelope least squares (ENV) model whose estimation is based on maximum normal likelihood, the estimation of the EHR model is through Generalized Method of Moments. The asymptotic normality of the EHR estimator is established, and it is shown that EHR is more efficient than HR. Moreover, EHR is more efficient than ENV when the error distribution is heavy-tailed, while maintaining a small efficiency loss when the error distribution is normal. Moreover, our theory also covers the heteroscedastic case in which the error may depend on the covariates. Extensive simulation studies confirm the messages from the asymptotic theory. EHR is further illustrated on a real dataset.

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