This is a text (divided into two volumes) for a two semester course in
Mathematical Statistics at the Senior/Graduate level. The two main
pedagogical aspects in these Volumes are: (i) the material is designed
in lessons (each for a 50 minute class) with complementary exercises and
home work. (ii) although the material is traditional, great care is
exerted upon self-contained, rigorous and complete presentations. An
elementary introduction to characteristic functions and probability
measures and intergration, but not general measure theory in Volume I,
allows a complete proof of some central limit theorems and a rigorous
treatment of asymptotic of statistical inference. But students need to
be familiar only with such things as Jacobians and eigenvalues of
matrices. Volume II: Statistical Inference is designed for the second
semester and contains a rigorous introduction to Mathematical
Statistics, from random samples to asymptotic theory of statistical
inference.