Advanced Mathematical Statistics

Stochastic convergence. Projections. U-statistics. Concentration inequalities. Uniform laws. Empirical process theory. Delta method. Functional delta method. Contiguity. Local asymptotic normality. Efficiency of estimators. Efficiency of tests. Applications: Nonparametric regression. Nonparametric density estimation. M-estimators. Bootstrap estimators.

Basic Information

Workload
45 hours
Requirements
Mathematical Statistics, Measure, Integration and Probability, Functional Analysis: Fundamentals

Mandatory: 

  • Van der Vaart, A. W. (1998). Asymptotic statistics (Vol. 3). Cambridge university press.
  • Pollard, D. (1984). Convergence of stochastic processes. Springer. Available on-line at http://www.stat.yale.edu/~pollard/1984book/.
  • Kosorok, M. R. (2008). Introduction to empirical processes and semiparametric inference. New York: Springer.

Complementary: 

  • Van de Geer, S. A., & van de Geer, S. (2000). Empirical Processes in M-estimation (Vol. 6). Cambridge university press.
  • Van Der Vaart, A. W., & Wellner, J. A. (1996). Weak convergence and empirical processes(pp. 16-28). Springer, New York, NY.
  • Le Cam, L., & Yang, G. L. (2012). Asymptotics in statistics: some basic concepts. Springer Science & Business Media.
  • Serfling, R. J. (2009). Approximation theorems of mathematical statistics (Vol. 162). John Wiley & Sons.
  • Billingsley, P. (1999). Convergence of probability measures. John Wiley & Sons.