Theory and Methods of Statistical Inference Syllabus

PhD School in Statistics XXII cycle, 2007

Theory and Methods of Statistical Inference (A. Salvan and B. Liseo, N. Sartori, A.Tancredi, L. Ventura)

Syllabus Statistical models and likelihood: Review (parametric, semiparametric and nonparametric models). Approaches to statistical inference. Data and model reduction: Sufficiency and conditioning upon distribution constant statistics. Pivotal quantities and estimating equations. Basic techniques: Moments, cumulants and generating functions. Basic ideas on asymptotic techniques. Review and further results on asymptotic likelihood theory. Empirical distribution function. Optimal inference procedures. Data and model reduction in the presence of nuisance prameters: Marginal and conditional likelihoods, profile and adjusted profile likelihoods, quasi-likelihood, empirical likelihood. Exponential families: Mathematical theory. Parameterizations and variance function. Optimal and likelihood inference. Generalized linear models: Exponential dispersion families. Generalized linear models, important examples, inference, quasi-likelihood. Group families: Group families as an extension of scale and location families. Mathematical theory. Optimal and likelihood inference. Some nonparametric problems. Robust inference: Statistical functionals, influence function, classes of robust estimators (M, L and Hampel estimators) and their approximate distributions, robustness and hypothesis testing, robust inference for regression models. Bayesian inference: Statistical models and prior information. Inference based on the posterior distribution. Chioce of the prior distribution: Jeffrey’s rule and reference priors. Point and interval estimation. Hypothesis testing and the Bayes factor. General linear model. Variable selection in multiple regression. Markov Chain Monte Carlo methods for Bayesian inference.

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Lectures and topics date 29/03/07 30/03/07 03/04/07 04/04/07 11/04/07 12/04/07 13/04/07 13/04/07 14/04/07 17/04/07 19/04/07

ore ore ore ore ore ore ore ore ore ore ore

11.00-13.00 9.30-11.30 9.00-11.00 11.00-13.00 11.00-13.00 15-18 9.30-12.30 15.00-18.00 9.30-12.30 9.00-11.00 11.00-13.00

20/04/07 24/04/07 26/04/07 27/04/07 02/05/07 04/05/07 04/05/07 08/05/07 09/05/07 11/05/07 15/05/07 15/05/07

ore ore ore ore ore ore ore ore ore ore ore ore

9.30-11.30 9.00-11.00 11.00-13.00 9.00-11.00 11.00-13.00 9.30-10.30 11.00-12.00 10.00-12.00 11.00-13.00 9.30-11.30 9.00-11.00 16.30-18.30

16/05/07 ore 11.00-13.00 18/05/07 22/05/07 23/05/07 25/05/07 28/05/07

ore 9.30-11.30 ore 9.00-11.00 ore 11.00-13.00 ore 9.00-11.00 ore 10.30-12.30 15.00-17.00 29/05/07 ore 10.30-12.30 30/05/07 ore 11.00-13.00 31/05/07 ore 9.00-11.00 Where unspecified, lectures

topic statistical models: data variability and sampling variability generating functions, approximation of moments, transformations review/exercises likelihood: observed quantities, exact properties, inference likelihood: examples Bayesian inference (Prof. B.Liseo, Univ. Rome La Sapienza) Bayesian inference (Prof. B.Liseo) Bayesian inference (Prof. B.Liseo) Bayesian inference (Prof. B.Liseo) review/exercises lab. on “likelihood: graphical and numerical techniques with R, I ” (Dr.N.Sartori, Univ. Ca’ Foscari Venice) data and model reduction: sufficiency, conditioning data and model reduction: sufficiency, conditioning review/exercises point estimation: optimality and likelihood theory point estimation: optimality and likelihood theory seminar “Sweave+Latex: a tutorial” (Dr.N.Sartori) exercises hypothesis testing and confidence regions: optimality and likelihood theory hypothesis testing and confidence regions: optimality and likelihood theory likelihood inference with nuisance parameters likelihood inference with nuisance parameters lab. on “likelihood: graphical and numerical techniques with R, II” (Dr.N.Sartori) exponential families: general theory; exponential dispersion families and generalized linear models exponential families: inference group families: general theory group families: inference review/exercises MCMC methods for Bayesian inference (Dr.A.Tancredi, Univ. Rome La Sapienza) MCMC methods for Bayesian inference (Dr.A.Tancredi) robust methods (Prof. L.Ventura) robust methods (Prof. L.Ventura) are given by A.Salvan.

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References Barndorff-Nielsen, O.E. and Cox, D.R. (1994). Inference and Asymptotics. Chapman and Hall, London. Cox, D.R. (2006). Principles of Statistical Inference, Cambridge University Press, Cambridge. Cox, D.R. and Hinkley, D.V. (1974). Theoretical Statistics. Chapman and Hall, London. Davison, A.C. (2003). Statistical Models. Cambridge University Press, Cambridge. Hampel, F.R., Ronchetti, E., Rousseeuw, P.J., and Stahel, W.A. (1986). Robust Statistics: the Approach based on Influence Functions. Wiley, New York. Lehmann, E.L. (1983). Theory of Point Estimation, Wiley, New York. Lehmann, E.L. (1986). Testing Statistical Hypotheses, 2-nd ed.. Wiley, New York. Liseo, B. (2007). Introduzione alla Statistica Bayesiana, in preparazione. McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models, 2-nd ed.. Chapman and Hall, London. O’Hagan, A. and Forster, J. (2004) Bayesian Inference (Seconda edizione). Edward Arnold, London. Pace, L. and Salvan, A. (1996). Teoria della Statistica: Metodi, Modelli, Approssimazioni Asintotiche. Cedam, Padova. Pace, L. and Salvan, A. (1997). Principles of Statistical Inference from a neo-Fisherian Perspective. World Scientific, Singapore. Robert C.P. and Casella G. (2004) Monte Carlo Statistical Methods (Seconda edizione). Springer, New York Severini, T.A. (2000). Likelihood Methods in Statistics. Oxford University Press, Oxford. Severini, T.A. (2005). Elements of Distribution Theory. Cambridge University Press, Cambridge. van der Vaart, A.W. (1998). Asymptotic Statistics, Cambridge University Press, Cambridge. Wasserman, L. (2004). All of Statistics. Springer, New York. Welsh, A.H. (1996). Aspects of Statistical Inference. Wiley, New York. Young, G.A. and Smith, R.L. (2005). Essentials of Statistical Inference. Cambridge University Press, Cambridge.

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