Fetching the paper…

Reading the bibliography…

2012

Bayesian sandwich posteriors for pseudo-true parameters

Hoff, Peter, Wakefield, Jon

Original
PDF
Post on X

Understand

Under model misspecification, the MLE generally converges to the pseudo-true parameter, the parameter corresponding to the distribution within the model that is closest to the distribution from which the data are sampled.

In many problems, the pseudo-true parameter corresponds to a population parameter of interest, and so a misspecified model can provide consistent estimation for this parameter.
Furthermore, the well-known sandwich variance formula of Huber(1967) provides an asymptotically accurate sampling distribution for the MLE, even under model misspecification.
However, confidence intervals based on a sandwich variance estimate may behave poorly for low sample sizes, partly due to the use of a plug-in estimate of the variance.

Bayesian sandwich posteriors for pseudo-true parameters · Around

Built on

Posterior distributions for multivariate normal parameters
Geisser, S. and J. Cornfield (1963) · 1963
Earlier work this paper cites.
The behavior of maximum likelihood estimators under non-standard conditions
Huber, P. (1967) · 1967
Earlier work this paper cites.
A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity
White, H. (1980) · 1980
Earlier work this paper cites.
Maximum likelihood estimation of misspecified models
White, H. (1982) · 1982
Earlier work this paper cites.
Pseudo-maximum likelihood methods: theory
Gourieroux, C., A. Montfort, and A. Trognon (1984) · 1984
Earlier work this paper cites.

Similar

Longitudinal data analysis using generalized linear models
Liang, K. and S. Zeger (1986) · 1986
Cited alongside, same era.
Model robust confidence intervals using maximum likelihood estimators
Royall, R. (1986) · 1986
Cited alongside, same era.
Longitudinal data analysis for discrete and continuous outcomes
Zeger, S. and K. Liang (1986) · 1986
Cited alongside, same era.
A note on the efficiency of sandwich covariance matrix estimation
Kauermann, G. and R. Carroll (2001) · 2001
Cited alongside, same era.
Bayes factors based on test statistics
Johnson, V. (2005) · 2005
Cited alongside, same era.

Then

Extending the rank likelihood for semiparametric copula estimation
Hoff, P. D. (2007) · 2007
Later among the works it cites.
Bayes factors for genome-wide association studies: comparison with p-values
Wakefield, J. (2009) · 2009
Later among the works it cites.
Risk of bayesian inference in misspecified models, and the sandwich covariance matrix
Müller, U. (2011) · 2011
Later among the works it cites.
Bayesian inference with misspecified models
Walker, S. G. (2013) · 2013
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…