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Multiparametric Statistics (Hardcover)
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Multiparametric Statistics (Hardcover)
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This monograph presents mathematical theory of statistical models
described by the essentially large number of unknown parameters,
comparable with sample size but can also be much larger. In this
meaning, the proposed theory can be called "essentially
multiparametric." It is developed on the basis of the Kolmogorov
asymptotic approach in which sample size increases along with the
number of unknown parameters.
This theory opens a way for solution of central problems of
multivariate statistics, which up until now have not been solved.
Traditional statistical methods based on the idea of an infinite
sampling often break down in the solution of real problems, and,
dependent on data, can be inefficient, unstable and even not
applicable. In this situation, practical statisticians are forced
to use various heuristic methods in the hope the will find a
satisfactory solution.
Mathematical theory developed in this book presents a regular
technique for implementing new, more efficient versions of
statistical procedures. Near exact solutions are constructed for a
number of concrete multi-dimensional problems: estimation of
expectation vectors, regression and discriminant analysis, and for
the solution to large systems of empiric linear algebraic
equations. It is remarkable that these solutions prove to be not
only non-degenerating and always stable, but also near exact within
a wide class of populations.
In the conventional situation of small dimension and large sample
size these new solutions far surpass the classical, commonly used
consistent ones. It can be expected in the near future, for the
most part, traditional multivariate statistical software will be
replaced by the always reliable and more efficient versions of
statistical procedures implemented by the technology described in
this book.
This monograph will be of interest to a variety of specialists
working with the theory of statistical methods and its
applications. Mathematicians would find new classes of urgent
problems to be solved in their own regions. Specialists in applied
statistics creating statistical packages will be interested in more
efficient methods proposed in the book. Advantages of these methods
are obvious: the user is liberated from the permanent uncertainty
of possible instability and inefficiency and gets algorithms with
unimprovable accuracy and guaranteed for a wide class of
distributions.
A large community of specialists applying statistical methods to
real data will find a number of always stable highly accurate
versions of algorithms that will help them to better solve their
scientific or economic problems. Students and postgraduates will be
interested in this book as it will help them get at the foremost
frontier of modern statistical science.
- Presents original mathematical investigations
and open a new branch of mathematical statistics
- Illustrates a technique for developing always stable and
efficient versions of multivariate statistical analysis for
large-dimensional problems
- Describes the most popular methods some near exact solutions;
including algorithms of non-degenerating large-dimensional
discriminant and regression analysis
General
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