STA 4508: Topics in Likelihood Inference Spring 2016

SS 1080 Tuesdays 2-5 pm. First class January 12.
On March 1 we meet in SS 6004

Inference based on the likelihood function: derived quantities, limiting distributions, approximations to posterior distributions;
Adjusted profile log-likelihoods: motivation, derivation, examples;
Composite likelihood: definition, summary statistics, asymptotic theory; applications
Likelihood for semi-parametric and non-parametric models: proportional hazards regression, partially linear models, penalized likelihood;
An introduction to likelihood inference for p > n;
Simulated likelihoods, indirect 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.
(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.

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

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
van der Waart, A. (1998). Asymptotic Statistics Ch.25.
Owen, A. (2000). Empirical Likelihood Ch.2.
Hirosi, Y. (2011). Efficiency of profile likelihood in semi-parametric models. Ann. Inst. Stat. Math. 63, 1247-1275
Zeng, D. and Lin, D.Y. (2010). A general asymptotic theory for maximum likelihood estimation in semiparametric regression models with censored data.Stat. Sinica 20, 871-910
Andresen, A. and Spokoiny, V. (2014). Critical dimension in profile semiparametric estimation. Elect. J Statist. 8 3077-3125

Bühlmann, P. (2013) Statistical significance in high-dimensional linear models Bernoulli 19, 1212-1242.
Bühlmann, P., Kalisch, M. and Meier, L. (2014) High-dimensional statistics with a view toward applications in biology. Annual Review of Statistics and its Applications 1, 255-278.
Lockhart,R., Taylor, J., Tibshirani, R., Tibshirani, R. (2014) A significance test for the Lasso. Annals of Statistics 42, 413-468.
Portnoy, S. (1988). Asymptotic behaviour of likelihood methods for exponential families when the number of parameters tends to infinity. Ann. Statist. 16, 356-366. (also Portnoy 1984 and 1985, AoS.)

Slides (corrected Feb 2)
Exercises
Varin/Czado Biostatistics paper
Varin/Czado supplement
Varin/Czado R library (Better to download directly from publisher; it's the 4th supplementary filfe in the list.)