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STA 4508: Topics in Likelihood Inference Spring 2014
Topics
- Inference based on the likelihood function: derived quantities, limiting
distributions, marginal and conditional likelihood, Laplace approximation
to posterior distributions;
- Adjusted profile log-likelihoods: motivation, derivation, examples;
- Composite likelihood: definition, summary statistics, asymptotic theory;
- Quasi-likelihood: generalized linear models, generalized
estimating equations;
- Semi-parametric likelihoods: proportional hazards regression,
partially linear models, penalized likelihood;
- Empirical likelihood: definition, examples, inference
Running list of references and background reading
Review Papers
- Reid, N. (2013). Aspects of likelihood inference Bernoulli 19, 1404-1418.
- Reid, N. (2010). Likelihood
Inference Wiley Interdisciplinary Reviews in Computational Statistics 5, 517-525.
(I need to use Preview to view this, rather than Adobe.)
- Reid, N. (2011). Likelihood International
Encyclopedia of Statistical Science, Part 5, 455-459.
- Reid, N. (2000). Likelihood.
J. Am. Stat. Assoc., 95, 1335-1340.
Likelihood Basics
- Davison, A.C. (2003) Statistical Models (SM) Cambridge University Press. -- Ch 4
- Barndorff-Nielsen, O.E. and Cox, D.R. (1994) Inference and Asymptotics
(BNC) Chapman and Hall. -- Ch 2.2
- Cox, D.R. and Hinkley, D.V. (1974) Theoretical Statistics (CH)
Chapman and Hall. -- Ch 2.1 (i), (ii)
- Cox, D.R. (2006). Principles of Statistical Inference
(Cox) -- Ch.2.1
Marginal/conditional/profile/adjusted likelihood
- Properties of profile likelihood: BNC -- Ch 3.4-7
- Marginal and conditional likelihood functions: SM -- Ch 12.2,3
- Adjustments to profile likelihood: SM -- 12.3; BNC -- 8.2; Cox & Reid (1987). JRSS B, 49, 1--39.
- Laplace approximation: SM -- Ch 11.3; Tierney & Kadane (1986), JASA 81, 82--86.
Composite likelihood
- Varin (2008). Advances in Statistical Analysis On composite marginal likelihoods. Available here
- Varin, Reid and Firth (2011). Statistica Sinica An overview of composite likelihood methods. Available here
- Varin and Czado (2010). Biostatistics A mixed autoregressive probit model for ordinal longitudinal data. Available here
- Cox and Reid (2004). Biometrika A note on pseudolikelihood constructed from marginal densities. Available here
- Renard et al. (2004). Computational Statistics and Data Analysis A pairwise likelihood approach to estimation in multilevel probit models. Available here
Quasi-likelihood
- Firth, D. (1991). Generalized linear models. in Statistical Theory and Modelling: In Honour of Sir David Cox, FRS, eds. D.V. Hinkley, N. Reid and E.J. Snell, pp.55--82. London:Chapman & Hall.
- McCullagh, P. (1991). Quasi-likelihood and estimating functions. in Statistical Theory and Modelling, pp.265-286.
- McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. Ch. 9.
- Davison, A.C. (2003). Statistical Models Ch. 10.6.
Partial Likelihood
- Oakes, D. (1991). Life table analysis. in Statistical Theory and Modelling, pp. 107-128.
- Davison, A.C. (2003) Statistical Models Ch.5.4; 10.8.
- Cox, D.R. (1972). Regression models and life tables. JRSS B.
- Cox, D.R. (1975). Partial likelihood. Biometrika.
- Murphy, S.A. and van der Waart, A. (2000). On profile likelihood. JASA.
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