Application of shrinkage estimation in linear regression models with autoregressive errors

Thomson, T.; Hossain, Shakhawat; Ghahramani, M.

doi:10.1080/00949655.2014.971326

Cited by 9 publications

(1 citation statement)

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“…Shrinkage estimation methods have been studied for some time series regression models. Thomson, Hossain & Ghahramani (2014) developed shrinkage estimators and compared them to penalty‐based estimation procedures for linear regression models with autoregressive errors. Fallahpour, Ahmed & Doksum () considered shrinkage and penalty estimation strategies for partial linear regression models when the error term is a first‐order random coefficient autoregressive error term.…”

Section: Introductionmentioning

confidence: 99%

Efficient estimation for time series following generalized linear models

Thomson

Hossain

Ghahramani

2016

Aust. N. Z. J. Stat.

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In this paper, we consider James-Stein shrinkage and pretest estimation methods for time series following generalized linear models when it is conjectured that some of the regression parameters may be restricted to a subspace. Efficient estimation strategies are developed when there are many covariates in the model and some of them are not statistically significant. Statistical properties of the pretest and shrinkage estimation methods including asymptotic distributional bias and risk are developed. We investigate the relative performances of shrinkage and pretest estimators with respect to the unrestricted maximum partial likelihood estimator (MPLE). We show that the shrinkage estimators have a lower relative mean squared error as compared to the unrestricted MPLE when the number of significant covariates exceeds two. Monte Carlo simulation experiments were conducted for different combinations of inactive covariates and the performance of each estimator was evaluated in terms of its mean squared error. The practical benefits of the proposed methods are illustrated using two real data sets.

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Section: Introductionmentioning

confidence: 99%