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A Course in Large Sample Theory is presented in four parts. The
first treats basic probabilistic notions, the second features the
basic statistical tools for expanding the theory, the third
contains special topics as applications of the general theory, and
the fourth covers more standard statistical topics. Nearly all
topics are covered in their multivariate setting. The book is
intended as a first year graduate course in large sample theory for
statisticians. It has been used by graduate students in statistics,
biostatistics, mathematics, and related fields. Throughout the book
there are many examples and exercises with solutions. It is an
ideal text for self study.
Game theory is a fascinating subject. We all know many entertaining
games, such as chess, poker, tic-tac-toe, bridge, baseball,
computer games - the list is quite varied and almost endless. In
addition, there is a vast area of economic games, discussed in
Myerson (1991) and Kreps (1990), and the related political games
[Ordeshook (1986), Shubik (1982), and Taylor (1995)]. The
competition between firms, the conflict between management and
labor, the fight to get bills through congress, the power of the
judiciary, war and peace negotiations between countries, and so on,
all provide examples of games in action. There are also
psychological games played on a personal level, where the weapons
are words, and the payoffs are good or bad feelings [Berne (1964)].
There are biological games, the competition between species, where
natural selection can be modeled as a game played between genes
[Smith (1982)]. There is a connection between game theory and the
mathematical areas of logic and computer science. One may view
theoretical statistics as a two-person game in which nature takes
the role of one of the players, as in Blackwell and Girshick (1954)
and Ferguson (1968).Games are characterized by a number of players
or decision makers who interact, possibly threaten each other and
form coalitions, take actions under uncertain conditions, and
finally receive some benefit or reward or possibly some punishment
or monetary loss. In this text, we present various mathematical
models of games and study the phenomena that arise. In some cases,
we will be able to suggest what courses of action should be taken
by the players. In others, we hope simply to be able to understand
what is happening in order to make better predictions about the
future.
A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.
The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.
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