Efficient estimation for time series following generalized linear models

Abstract

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.

Model Selection and Post Selection to Improve the Estimation of the ARCH Model

“…Al-Momani et al (2016) proposed shrinkage and penalty estimators for the spatial error model. Thomson et al (2016) investigated the relative performances of pretest and shrinkage estimators for time series following generalized linear models. In all these cases, shrinkage estimators outperformed classical estimators.…”

Shrinkage estimation of the exponentiated Weibull regression model for time‐to‐event data

“…The maximum likelihood method is thus far the most widely used technique for statistical inference, though there is a considerable body of research of improving the maximum likelihood estimators in terms of asymptotic efficiency. For example, there has recently been considerable attention on applying James–Stein shrinkage ideas to parameter estimation in parametric and semiparametric regression models (Hossain & Ahmed, 2012; Lian, 2012; Thomsom, Hossain, & Ghahramani, 2016; Xua & Yanga, 2012). It was inspired by Stein's result that if the dimension of the vector of regression parameters is three or more, the maximum likelihood (ML) estimators can be improved by incorporating auxiliary/prior information into the estimation procedure (Judge & Mittelhammaer, 2004).…”

“…It was inspired by Stein's result that if the dimension of the vector of regression parameters is three or more, the maximum likelihood (ML) estimators can be improved by incorporating auxiliary/prior information into the estimation procedure (Judge & Mittelhammaer, 2004). Many authors demonstrated that in a regression setting, the shrinkage estimators outperform the classical estimators in terms of the mean squared error (Chen & Nkurunziza, 2015; Thomsom et al, 2016). Hansen (2016) showed that the asymptotic risk (expected loss of the asymptotic distribution) of a feasible shrinkage estimator is strictly smaller than that of the maximum likelihood estimator uniformly over all parameter sets local to the shrinkage parameter space.…”

Estimation strategy of multilevel model for ordinal longitudinal data

“…Zeng and Hill (2016) explored the properties of pretest and shrinkage estimators for random parameters logit models. Many articles have been devoted to the study of pretest and shrinkage estimators in parametric and semi-parametric linear models for uncorrelated data, including Thomson et al (2016), Hossain et al (2015), Lian (2012), and among others.…”