Multivariate Calculation

Author : R.H. Farrell
Publisher : Springer Science & Business Media
ISBN 13 : 1461385288
Total Pages : 392 pages
Book Rating : 4.88/5 ( download)

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Download or read book Multivariate Calculation written by R.H. Farrell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like some of my colleagues, in my earlier years I found the multivariate Jacobian calculations horrible and unbelievable. As I listened and read during the years 1956 to 1974 I continually saw alternatives to the Jacobian and variable change method of computing probability density functions. Further, it was made clear by the work of A. T. James that computation of the density functions of the sets of roots of determinental equations required a method other than Jacobian calculations and that the densities could be calculated using differential forms on manifolds. It had become clear from the work ofC S. Herz and A. T. James that the expression of the noncentral multivariate density functions required integration with respect to Haar measures on locally compact groups. Material on manifolds and locally compact groups had not yet reached the pages of multivariate books of the time and also much material about multivariate computations existed only in the journal literature or in unpublished sets oflecture notes. In spirit, being more a mathematician than a statistician, the urge to write a book giving an integrated treatment of these topics found expression in 1974-1975 when I took a one year medical leave of absence from Cornell University. During this period I wrote Techniques of Multivariate Calculation. Writing a coherent treatment of the various methods made obvious re quired background material.

Author : R. H. Farrell
Publisher : Springer
ISBN 13 : 3540382275
Total Pages : 347 pages
Book Rating : 4.70/5 ( download)

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Download or read book Techniques of Multivariate Calculation written by R. H. Farrell and published by Springer. This book was released on 2006-11-14 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Brian Everitt
Publisher : Springer Science & Business Media
ISBN 13 : 1441996508
Total Pages : 284 pages
Book Rating : 4.03/5 ( download)

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Download or read book An Introduction to Applied Multivariate Analysis with R written by Brian Everitt and published by Springer Science & Business Media. This book was released on 2011-04-23 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.

Author : Alan Genz
Publisher : Springer Science & Business Media
ISBN 13 : 3642016898
Total Pages : 130 pages
Book Rating : 4.99/5 ( download)

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Download or read book Computation of Multivariate Normal and t Probabilities written by Alan Genz and published by Springer Science & Business Media. This book was released on 2009-07-09 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

Author : R. H. Farrell
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.93/5 ( download)

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Download or read book Techniques of Multivariate Calculation written by R. H. Farrell and published by Lecture Notes in Mathematics. This book was released on 1976-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Thomas D. Wickens
Publisher : Psychology Press
ISBN 13 : 1317780221
Total Pages : 216 pages
Book Rating : 4.29/5 ( download)

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Download or read book The Geometry of Multivariate Statistics written by Thomas D. Wickens and published by Psychology Press. This book was released on 2014-02-25 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: A traditional approach to developing multivariate statistical theory is algebraic. Sets of observations are represented by matrices, linear combinations are formed from these matrices by multiplying them by coefficient matrices, and useful statistics are found by imposing various criteria of optimization on these combinations. Matrix algebra is the vehicle for these calculations. A second approach is computational. Since many users find that they do not need to know the mathematical basis of the techniques as long as they have a way to transform data into results, the computation can be done by a package of computer programs that somebody else has written. An approach from this perspective emphasizes how the computer packages are used, and is usually coupled with rules that allow one to extract the most important numbers from the output and interpret them. Useful as both approaches are--particularly when combined--they can overlook an important aspect of multivariate analysis. To apply it correctly, one needs a way to conceptualize the multivariate relationships that exist among variables. This book is designed to help the reader develop a way of thinking about multivariate statistics, as well as to understand in a broader and more intuitive sense what the procedures do and how their results are interpreted. Presenting important procedures of multivariate statistical theory geometrically, the author hopes that this emphasis on the geometry will give the reader a coherent picture into which all the multivariate techniques fit.

Author : Kohei Adachi
Publisher : Springer
ISBN 13 : 9811023417
Total Pages : 298 pages
Book Rating : 4.15/5 ( download)

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Download or read book Matrix-Based Introduction to Multivariate Data Analysis written by Kohei Adachi and published by Springer. This book was released on 2016-10-11 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

Author : R. H. Farrell
Publisher :
ISBN 13 : 9781461385295
Total Pages : 396 pages
Book Rating : 4.96/5 ( download)

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Download or read book Multivariate Calculation written by R. H. Farrell and published by . This book was released on 1984-12-03 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Timothy R.C. Read
Publisher : Springer Science & Business Media
ISBN 13 : 1461245788
Total Pages : 221 pages
Book Rating : 4.80/5 ( download)

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Download or read book Goodness-of-Fit Statistics for Discrete Multivariate Data written by Timothy R.C. Read and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistical analysis of discrete multivariate data has received a great deal of attention in the statistics literature over the past two decades. The develop ment ofappropriate models is the common theme of books such as Cox (1970), Haberman (1974, 1978, 1979), Bishop et al. (1975), Gokhale and Kullback (1978), Upton (1978), Fienberg (1980), Plackett (1981), Agresti (1984), Goodman (1984), and Freeman (1987). The objective of our book differs from those listed above. Rather than concentrating on model building, our intention is to describe and assess the goodness-of-fit statistics used in the model verification part of the inference process. Those books that emphasize model development tend to assume that the model can be tested with one of the traditional goodness-of-fit tests 2 2 (e.g., Pearson's X or the loglikelihood ratio G ) using a chi-squared critical value. However, it is well known that this can give a poor approximation in many circumstances. This book provides the reader with a unified analysis of the traditional goodness-of-fit tests, describing their behavior and relative merits as well as introducing some new test statistics. The power-divergence family of statistics (Cressie and Read, 1984) is used to link the traditional test statistics through a single real-valued parameter, and provides a way to consolidate and extend the current fragmented literature. As a by-product of our analysis, a new 2 2 statistic emerges "between" Pearson's X and the loglikelihood ratio G that has some valuable properties.

Author : Roger H. Farrell
Publisher : Springer Verlag
ISBN 13 : 9780387076959
Total Pages : 337 pages
Book Rating : 4.56/5 ( download)

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Download or read book Techniques of Multivariate Calculation written by Roger H. Farrell and published by Springer Verlag. This book was released on 1976-01-01 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: