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Владимир Спокойный

Modern Parametric Statistics

Course Schedule:

• February 10, 19-00 -- 20-30
  Basics of parametric statistics: maximum likelihood approach, exponential family, linear model. Properties of maximum likelihood, concentration and confidence sets, Gauss-Markov, Cramer-Rao and van Trees results.
• February 11, 19-00 -- 20-30
  Few chapters of modern parametrics: - Concentration and large deviations, - Fisher and Wilks expansions and corollaries.
• February 17, 19-00 -- 20-30
  Nonparametric function estimation: - White noise and regression models, generalized regression, density models. - Sieve approximation, modeling bias, bias-variance decomposition. - Model selection via unbiased risk estimation.
• February 18, 19-00 -- 20-30
  Penalized maximum likelihood and the problem of choosing the penalty: - Fisher and Wilks for penalized maximum likelihood. - Uniform confidence bands and concentration of the empirical risk. - Choice of tuning parameters by propagation idea.
• February 24, 19-00 -- 20-30
  Local parametric approach: - Applications to regression, generalized regression, density models. - Examples of local constant and local linear approximation. - Local Fisher and Wilks results.
• February 25, 19-00 -- 20-30
  Choice of the bandwidth in local parametric estimation using propagation approach. - Sizer and Intersection-of-confidence-intervals idea and local model selection. - Choice of tuning parameters by propagation. - Propagation property and oracle risk bound.

Exam dates

Course Materials:

• Textbook: http://premolab.ru/sites/default/files/stat.pdf