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This is the first half of a text for a two semester course in
mathematical statistics at the senior/graduate level for those who
need a strong background in statistics as an essential tool in
their career. To study this text, the reader needs a thorough
familiarity with calculus including such things as Jacobians and
series but somewhat less intense familiarity with matrices
including quadratic forms and eigenvalues. For convenience, these
lecture notes were divided into two parts: Volume I, Probability
for Statistics, for the first semester, and Volume II, Statistical
Inference, for the second. We suggest that the following
distinguish this text from other introductions to mathematical
statistics. 1. The most obvious thing is the layout. We have
designed each lesson for the (U.S.) 50 minute class; those who
study independently probably need the traditional three hours for
each lesson. Since we have more than (the U.S. again) 90 lessons,
some choices have to be made. In the table of contents, we have
used a * to designate those lessons which are "interesting but not
essential" (INE) and may be omitted from a general course; some
exercises and proofs in other lessons are also "INE." We have made
lessons of some material which other writers might stuff into
appendices. Incorporating this freedom of choice has led to some
redundancy, mostly in definitions, which may be beneficial.
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.
This is the first half of a text for a two semester course in
mathematical statistics at the senior/graduate level for those who
need a strong background in statistics as an essential tool in
their career. To study this text, the reader needs a thorough
familiarity with calculus including such things as Jacobians and
series but somewhat less intense familiarity with matrices
including quadratic forms and eigenvalues. For convenience, these
lecture notes were divided into two parts: Volume I, Probability
for Statistics, for the first semester, and Volume II, Statistical
Inference, for the second. We suggest that the following
distinguish this text from other introductions to mathematical
statistics. 1. The most obvious thing is the layout. We have
designed each lesson for the (U.S.) 50 minute class; those who
study independently probably need the traditional three hours for
each lesson. Since we have more than (the U.S. again) 90 lessons,
some choices have to be made. In the table of contents, we have
used a * to designate those lessons which are "interesting but not
essential" (INE) and may be omitted from a general course; some
exercises and proofs in other lessons are also "INE." We have made
lessons of some material which other writers might stuff into
appendices. Incorporating this freedom of choice has led to some
redundancy, mostly in definitions, which may be beneficial.
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