NOTE:
Starred points* will be actually covered according to available time 

1.       Basic asymptotic approximation tools
from probability theory (2h)

-          Modes of convergence and their basic properties

-          Convergence of moments and uniform
integrability *

-          Representation theorem: elementary
version *

-          Convergence of transformed/perturbed
random variables

-          Laws of large numbers

-          Central limit theorems

-          Approximation error in the central
limit theorem *

2.       Basic classification of statistical
models: parametric, nonparametric, semiparametric

3.       Empirical distribution function (EDF)
and its properties (2 h)

-          Definition and elementary properties

-          Glivenko-Cantelli theorem

-          Large deviations for empirical
distribution functions: the Sanov theorem *

-          The empirical process: basic weak
convergence results *

4.       Asymptotics for the Maximum Likelihood
Estimators (MLEs) (6 h)

-          Consistency of the global maximizer
of the likelihood function: the Wald approach

-          Consistency and asymptotic normality
of roots of the likelihood equations

-          Asymptotic efficiency issues

-          Multidimensional extensions

5.       Multiple roots of likelihood equation(s)
(4 h)

-          The problem of multiple roots

-          One-step Newton-Raphson method

-          Multidimensional extensions

6.        M-estimators (6 h) *

-          Basic definitions and examples

-          Consistency of M-estimators

-          Asymptotic
normality of M-estimators