Focused information criterion and model averaging for generalized additive partial linear models

By Xinyu Zhang, Hua Liang. 2011

161 citations recorded by the source corpus.

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/720f094d283e04523e0531bd9124c4e0d0921984

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In Control and Systems Engineering

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Citations in the corpus

Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models (2016, methodology): “These methods are also advocated by Hjort and Claeskens (2003), Claeskens et al. (2006), and Zhang and Liang (2011).”
Weighted‐Average Least Squares (WALS): A Survey (2016, methodology): “…models (Claeskens et al., 2006); models for survival analysis (Hjort and Claeskens, 2006); generalized additive partial linear models (Zhang and Liang, 2011); Tobit models (Zhang et al., 2012); multinomial and ordered logit models (Wan et al., 2014); and linear mixed-effects models (Zhang et…”
Model averaging and weight choice in linear mixed-effects models (2014, methodology): “Following their work, efforts have been invested to study model averaging in, for example, semiparametric models (Claeskens & Carroll, 2007) and generalized partially linear additive models (Zhang & Liang, 2011).”
Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold (2012, methodology): “More recently, Bartolucci and Lupparelli ( 2008 ) proposed an FIC for selecting capture-recapture models, and Zhang and Liang ( 2011 ) developed an FIC for the generalized additive partial linear model.”
Model averaging by jackknife criterion in models with dependent data (2013, background): “…frequentist standpoint were made by Buckland et al. (1997), Yang (2001), Hjort and Claeskens (2003, 2006), Yuan and Yang (2005), Hansen (2007, 2008), Goldenshluger (2009), Schomaker et al. (2010), Wan et al. (2010), Liang et al. (2011), Zhang and Liang (2011), Zhang et al. (2012), among others.”
INFERENCE AFTER MODEL AVERAGING IN LINEAR REGRESSION MODELS (2018, unknown): “In contrast to Bayesian model averaging, there is a growing body of literature on frequentist model averaging, including information criterion weighting (Buckland et al., 1997; Hjort and Claeskens, 2003a; Zhang and Liang, 2011; Zhang et al., 2012), adaptive regression by mixing models (Yang, 2000, 2”
Model averaging based on leave-subject-out cross-validation (2016, methodology): “Recent years have also witnessed a booming development of frequentist model averaging methods such as weighting strategy based on the scores of information criteria (Buckland et al., 1997; Hjort and Claeskens, 2003, 2006; Zhang and Liang, 2011; Zhang et al., 2012; Xu et al., 2014), the adaptive regr”