With the advent of powerful computing and the availability of massive sets of data, statistics has become a valuable tool in numerous applications. This course covers the basics of advanced mathematical statistics, both classical and modern.

  • Review of basic probability
  • Parametric models, linear models, variable selection
  • Estimation: criteria and construction of estimators, maximum likelihood, asymptotics
  • Hypothesis testing, multiple hypotheses testing
  • Non parametric models, empirical distribution function, jackknife and bootstrap, non-parametric testing, density and regression estimation
  • Classification: discriminant analysis, support vector machines, multivariate analysis, EM algorithm and simulation including Monte Carlo Markov Chain

The level and detailed content of the course will be determined along with the students according to their background and interests.

Prerequisite: At least one good course in probability, and some basic statistics.
Larry Goldstein and Uwe Schmock

Structure and Evaluation

First week quiz: percentiles, out 90 points total: 25th: 12, median: 35, 75th: 54
Midterm: 30% scores: 26, 30, 41, 43, 55, 55, 58, 59, 62, 65, 67 Solutions
Final Exam: 45%
Course participation: 25%


Course Text

All of Statistics: A concise course in Statistical Inference, by Larry Wasserman.

Additional References

  • Mathematical Statistics: Basic Ideas and Selected Topics, by Peter Bickel and Kjell Doksum
  • A Course in Large Sample Theory, by Thomas Ferguson

Links of Interest

Benford’s lawSimple ExplanationBasic Theory of Benford’s law (for scale invariance, see Example 4.19 on page 42)
Formula for one dimensional normal density
Box Muller Transformation
Perugia Web Cam, Piazza IV novembre