STA 4508: Topics in Likelihood Inference Spring 2014

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

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.
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Reid, N. (2011). Likelihood International Encyclopedia of Statistical Science, Part 5, 455-459.
Reid, N. (2000). Likelihood. J. Am. Stat. Assoc., 95, 1335-1340.

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

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.

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

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.

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.