Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models

Zhang, Xinyu; Yu, Dalei; Zou, Guohua; Liang, Hua

doi:10.1080/01621459.2015.1115762

Cited by 140 publications

(85 citation statements)

References 34 publications

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“…Under conditions C.1–C.4, we can follow the proof of theorem 3 of Zhang, Yu, Zou, and Liang () and show that the post‐screened model‐averaging estimator based on the candidate model set

M^{s}

still achieves the asymptotic optimality, namely

\frac{L_{A} ({\hat{w}}^{s})}{\inf_{w \in W} L_{A} (w)} \to 1 .

Since the individual estimator is typically screened out by this procedure, this optimality theorem provides particular theoretical support for post‐screened model‐averaging estimators because of condition C.3.…”

Section: Shrinking Model Spacementioning

confidence: 65%

“…Under conditions C.1-C.4, we can follow the proof of theorem 3 of Zhang, Yu, Zou, and Liang (2016) and show that the post-screened model-averaging estimator based on the candidate model set  s still achieves the asymptotic optimality, namely…”

Section: Shrinking Model Spacementioning

confidence: 96%

“…There also exist various others methods to shrink the model space, such as top m model screening and ordering model screening (e.g., Claeskens, Croux, & Van Kerckhoven, 2006;Zhang et al, 2016), where the screening is mainly based on the values of information criteria. The bias-variance properties of these IC-based screening approaches are, however, less explicit compared to the proposed screening approach.…”

Section: Shrinking Model Spacementioning

confidence: 99%

See 2 more Smart Citations

To pool or not to pool: What is a good strategy for parameter estimation and forecasting in panel regressions?

Wang

Zhang

Paap

2019

J of Applied Econometrics

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Summary This paper considers estimating the slope parameters and forecasting in potentially heterogeneous panel data regressions with a long time dimension. We propose a novel optimal pooling averaging estimator that makes an explicit trade‐off between efficiency gains from pooling and bias due to heterogeneity. By theoretically and numerically comparing various estimators, we find that a uniformly best estimator does not exist and that our new estimator is superior in nonextreme cases and robust in extreme cases. Our results provide practical guidance for the best estimator and forecast depending on features of data and models. We apply our method to examine the determinants of sovereign credit default swap spreads and forecast future spreads.

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“…Under conditions C.1–C.4, we can follow the proof of theorem 3 of Zhang, Yu, Zou, and Liang () and show that the post‐screened model‐averaging estimator based on the candidate model set

M^{s}

still achieves the asymptotic optimality, namely

\frac{L_{A} ({\hat{w}}^{s})}{\inf_{w \in W} L_{A} (w)} \to 1 .

Section: Shrinking Model Spacementioning

confidence: 65%

Section: Shrinking Model Spacementioning

confidence: 96%

Section: Shrinking Model Spacementioning

confidence: 99%

See 1 more Smart Citation

To pool or not to pool: What is a good strategy for parameter estimation and forecasting in panel regressions?

Wang

Zhang

Paap

2019

J of Applied Econometrics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Other frequentist model averaging strategies include adaptive regression through mixing (Yang, 2001), jackknife model averaging (Hansen and Racine, 2012), heteroscedasticity robust model averaging (Liu and Okui, 2013), model averaging marginal regression (Chen et al, 2018;Li et al, 2015) and the plug-in method (Liu, 2015). Model averaging has also been extended to other contexts such as structural break models (Hansen, 2009), mixed effects models (Zhang et al, 2014), factor-augmented regression models (Cheng and Hansen, 2015), quantile regression models (Lu and Su, 2015), generalized linear models (Zhang et al, 2016) and missing data models (Fang et al, 2019;Zhang, 2013).…”

Section: Introductionmentioning

confidence: 99%

MALMEM: Model Averaging in Linear Measurement Error Models

Zhang

Carroll

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We develop model averaging estimation in the linear regression model where some covariates are subject to measurement error. The absence of the true covariates in this framework makes the calculation of the standard residual‐based loss function impossible. We take advantage of the explicit form of the parameter estimators and construct a weight choice criterion. It is asymptotically equivalent to the unknown model average estimator minimizing the loss function. When the true model is not included in the set of candidate models, the method achieves optimality in terms of minimizing the relative loss, whereas, when the true model is included, the method estimates the model parameter with root n rate. Simulation results in comparison with existing Bayesian information criterion and Akaike information criterion model selection and model averaging methods strongly favour our model averaging method. The method is applied to a study on health.

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“…There is a longstanding literature on Bayesian model averaging; see Hoeting, Madigan, Raftery & Volinsky (1999) for a comprehensive review. There is also a rapidly-growing literature on frequentist methods for model averaging, including Buckland, Burnhamn & Augustin (1997), Hansen (2007), Wan, Zhang & Zou (2010), Hansen & Racine (2012), Zhang & Wang (2015), Zhang, Zou & Carroll (2015) and Zhang, Yu, Zou & Liang (2016), among others.…”

Section: Introductionmentioning

confidence: 99%

Optimal Model Averaging of Varying Coefficient Models

Liu¹,

Li²,

Racine³

et al. 2019

STAT SINICA

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Abstract. We consider the problem of model averaging over a set of semiparametric varying coefficient models where the varying coefficients can be functions of continuous and categorical variables. We propose a Mallows model averaging procedure that is capable of delivering model averaging estimators with solid finite-sample performance. Theoretical underpinnings are provided, finite-sample performance is assessed via Monte Carlo simulation, and an illustrative application is presented. The approach is very simple to implement in practice and R code is provided in an appendix.

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Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models

Cited by 140 publications

References 34 publications

To pool or not to pool: What is a good strategy for parameter estimation and forecasting in panel regressions?

To pool or not to pool: What is a good strategy for parameter estimation and forecasting in panel regressions?

MALMEM: Model Averaging in Linear Measurement Error Models

Optimal Model Averaging of Varying Coefficient Models

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