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This text is an Elementary Introduction to Stochastic Processes in
discrete and continuous time with an initiation of the statistical
inference. The material is standard and classical for a first
course in Stochastic Processes at the senior/graduate level
(lessons 1-12). To provide students with a view of statistics of
stochastic processes, three lessons (13-15) were added. These
lessons can be either optional or serve as an introduction to
statistical inference with dependent observations. Several points
of this text need to be elaborated, (1) The pedagogy is somewhat
obvious. Since this text is designed for a one semester course,
each lesson can be covered in one week or so. Having in mind a
mixed audience of students from different departments (Math
ematics, Statistics, Economics, Engineering, etc.) we have
presented the material in each lesson in the most simple way, with
emphasis on moti vation of concepts, aspects of applications and
computational procedures. Basically, we try to explain to beginners
questions such as "What is the topic in this lesson?" "Why this
topic?," "How to study this topic math ematically?." The exercises
at the end of each lesson will deepen the stu dents' understanding
of the material, and test their ability to carry out basic
computations. Exercises with an asterisk are optional (difficult)
and might not be suitable for homework, but should provide food for
thought."
The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. The necessary mathematical tools are presented in Chapters 1 and 2. Chapters 3 to 6 deal with autoregressive processes in Hilbert and Banach spaces. Chapter 7 is devoted to general linear processes and Chapter 8 with statistical prediction. Implementation and numerical applications appear in Chapter 9. The book assumes a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the University of Paris 6 (Pierre et Marie Curie). He is Chief-Editor of Statistical Inference for Stochastic Processes and of Annales de l'ISUP, and Associate Editor of the Journal of Nonparametric Statistics. He is an elected member of the International Statistical Institute, and he has published about 100 papers or works on nonparametric statistics and five books including Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, Second Edition (Springer, 1998).
This book is devoted to the theory and applications of nonparametic functional estimation and prediction. Chapter 1 provides an overview of inequalities and limit theorems for strong mixing processes. Density and regression estimation in discrete time are studied in Chapter 2 and 3. The special rates of convergence which appear in continuous time are presented in Chapters 4 and 5. This second edition is extensively revised and it contains two new chapters. Chapter 6 discusses the surprising local time density estimator. Chapter 7 gives a detailed account of implementation of nonparametric method and practical examples in economics, finance and physics. Comarison with ARMA and ARCH methods shows the efficiency of nonparametric forecasting. The prerequisite is a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the Unviersity of Paris 6 (Pierre et Marie Curie). He is Editor-in-Chief of "Statistical Inference for Stochastic Processes" and an editor of "Journal of Nonparametric Statistics". He is an elected member of the International Statistical Institute. He has published about 90 papers or works in nonparametric statistics and four books.
This text is an Elementary Introduction to Stochastic Processes in
discrete and continuous time with an initiation of the statistical
inference. The material is standard and classical for a first
course in Stochastic Processes at the senior/graduate level
(lessons 1-12). To provide students with a view of statistics of
stochastic processes, three lessons (13-15) were added. These
lessons can be either optional or serve as an introduction to
statistical inference with dependent observations. Several points
of this text need to be elaborated, (1) The pedagogy is somewhat
obvious. Since this text is designed for a one semester course,
each lesson can be covered in one week or so. Having in mind a
mixed audience of students from different departments (Math
ematics, Statistics, Economics, Engineering, etc.) we have
presented the material in each lesson in the most simple way, with
emphasis on moti vation of concepts, aspects of applications and
computational procedures. Basically, we try to explain to beginners
questions such as "What is the topic in this lesson?" "Why this
topic?," "How to study this topic math ematically?." The exercises
at the end of each lesson will deepen the stu dents' understanding
of the material, and test their ability to carry out basic
computations. Exercises with an asterisk are optional (difficult)
and might not be suitable for homework, but should provide food for
thought."
This book offers a predominantly theoretical coverage of
statistical prediction, with some potential applications discussed,
when data and/ or parameters belong to a large or infinite
dimensional space. It develops the theory of statistical
prediction, non-parametric estimation by adaptive projection - with
applications to tests of fit and prediction, and theory of linear
processes in function spaces with applications to prediction of
continuous time processes.
This work is in the Wiley-Dunod Series co-published between
Dunod (www.dunod.com) and John Wiley and Sons, Ltd.
Generally, books on mathematical statistics are restricted to
the case of independent identically distributed random variables.
In this book however, both this case AND the case of dependent
variables, i.e. statistics for discrete and continuous time
processes, are studied. This second case is very important for
today's practitioners.Mathematical Statistics and Stochastic
Processes is based on decision theory and asymptotic statistics and
contains up-to-date information on the relevant topics of theory of
probability, estimation, confidence intervals, non-parametric
statistics and robustness, second-order processes in discrete and
continuous time and diffusion processes, statistics for discrete
and continuous time processes, statistical prediction, and
complements in probability.This book is aimed at students studying
courses on probability with an emphasis on measure theory and for
all practitioners who apply and use statistics and probability on a
daily basis.
This book is about sex. Our own sex. Sex is a problem: The problem
to get more sex. In the stone age, people used to solve this
problem using the easy way. If you were a man looking for an
intercourse, you just had to "go hunting" (hunting a girl, of
course ).
The girl used to awake in your cave, just to notice she was
officially married (with you). Nothing else was needed. Perhaps
some inquisitive reader may be wondering about her feelings....
Feelings? What was that?
Well, the fact is that the relationships between the sexes
started to be more complicated, and more, and more...until now. We
are living in a world that has changed its points of view
dramatically about sex. However, there is something that every age
in the history of the world had: Manners. Good manners, bad
manners, improper behavior and lack of sensibility are
characteristics of all human society. We are not exceptions to this
rule.
This book is focused in the works of William Shakespeare. However,
it is not a history book. It is a book of games inspired in his
figure.
A thematic puzzle is a kind of crossword puzzle where all the
questions are focused on a specific subject. For example: If we
speak about classic horror films, a question could be:
This book is about survival: Our own survival. Some time ago, I was
watching a medical motion picture where it was shown the case of
some people who had an accident in the mountains. Some of them
died. Some others survived. One of the conclusions was that there
is a personality that some people have, that makes them be able to
resist and survive in almost any circumstance. Some people call it
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