An asymptotic theory for model selection inference in general semiparametric problems

By Gerda Claeskens, Raymond J. Carroll. 2007

88 citations recorded by the source corpus.

SUMMARY Hjort & Claeskens (2003) developed an asymptotic theory for model selection, model averaging and subsequent inference using likelihood methods in parametric models, along with associated confidence statements. In this article, we consider a semiparametric version of this problem, wherein the likelihood depends on parameters and an unknown function, and model selection/averaging is to be applied to the parametric parts of the model. We show that all the results of Hjort & Claeskens hold in the semiparametric context, if the Fisher information matrix for parametric models is replaced by the semiparametric information bound for semiparametric models, and if maximum likelihood estimators for parametric models are replaced by semiparametric efficient profile estimators. Our methods of proof employ Le Cam’s contiguity lemmas, leading to transparent results. The results also describe the behaviour of semiparametric model estimators when the parametric component is misspecified, and also have implications for pointwise-consistent model selectors. Somekeywords: Akaike information criterion; Bayes information criterion; Efficient semiparametric estimation; Frequentist model averaging; Model averaging; Model selection; Profile likelihood; Semiparametric model.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/50e726006ddca4545b7ff7a81dff376b377c57bd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Edward I. George
2. Linda H. Zhao

In Management Science and Operations Research

1. Arun K. Kuchibhotla
2. Lawrence D. Brown
3. Edward I. George
4. Judith Rousseau
5. Mark F. J. Steel

In Statistics and Probability

1. Edward I. George
2. Arun K. Kuchibhotla
3. Lawrence D. Brown
4. Linda H. Zhao
5. Andreas Buja
6. Richard A. Berk
7. Judith Rousseau
8. Subhashis Ghosal

Citations in the corpus

• MMI: Multimodel inference or models with management implications? (2015, unknown): “Simulation and analytical results suggest that some modelaveraged interval estimators have similar width and coverage as those based on fitting a full model (Claeskens and Carroll 2007, Wang and Zhou 2013).”
• Valid post-selection inference in model-free linear regression (2020, background): “Ann. Statist., 41(2):802–837. Buehler, R. J. and Feddersen, A. P. (1963). Note on a conditional property of Student’s t. Ann. Math. Statist., 34:1098–1100. Buja, A., Berk, R., Brown, L., George, E., Pitkin, E., Traskin, M., Zhan, K., and Zhao, L. (2014). Models as Approximations, Part I: A Conspirac”
• Focused information criterion and model averaging for generalized additive partial linear models (2011, unknown): “If the link function g is identical and there is only one nonparametric component (i.e., p = 1), then the result of Theorem 1 will simplify to those of Theorems 3.1–3.4 of Claeskens and Carroll (2007) under the corresponding submodels.”
• Model averaging and weight choice in linear mixed-effects models (2014, unknown): “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).”