Master's degree in Statistics and Operations Research

Inference and Goodness-of-fit


poster_summer school_reilly -a3.jpgTítol del curs: Influence and goodness-of-fit
Impartit per: Federico O’Reilly

Llengua del curs: Anglès

Dates i horaris del curs: 14-20 juny 2011, de 10 a 14 h

Lloc: FME, aula 101

Tipus d'activitat i càrrega lectiva: Curs de 20 hores

Reconeixement acadèmic: 2,5 crèdits

Data de matrícula: del 16 de maig al 5 de juny de 2011


Presentation:
The objective of this course is to teach the student how to apply computational methods for statistical inference and in particular Bootstrap and Monte Carlo methods to estimate standard errors, construct confidence intervals, test hypotheses in a variety of statistical problems.

Course Content:
INFERENCE
  • Ingredients of an inference problem (and examples)
  • Likelihood
  • Su_ciency
  • Likelihood equivalence and minimal su_ciency
  • Fisher's likelihood principles
  • Point estimation
  • Minimum variance unbiased estimation
  • Cram_er-Rao lower bound approach
  • Rao-Blackwell theory, completeness
  • Miscellaneous on estimation (U-statistics)
  • Hypothesis testing
  • Neyman-Pearson lemma
  • Generalized likelihood ratio
     
GOODNESS-OF-FIT
  • Classical continuous case and EDF statistics
  • Asymptotics for EDF's, tables and corrections
  • Discrete case (di_erent approaches)
  • Generalized likelihood ratio and Kullback-Liebler's statistic
  • Location/scale families; probability plots and correlation
  • Shapiro-Wilk test for normality
  • Paradigm on large simulations vs asymptotic approximations
  • Review of simple case (continuous or discrete) and location/scale
  • Exact evaluation of p-values (conditional approach); bootstrap
  • Examples in continuous case (inverse Gaussian, gamma, von-Mises)
  • Examples in discrete case (Poisson, negative binomial and binomial)
     
Documents: