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.
This text for undergraduate students provides a foundation for resolving proofs dependent on n-dimensional systems. The two-part treatment begins with simple figures in n dimensions and advances to examinations of the contents of hyperspheres, hyperellipsoids, hyperprisms, etc. The second part explores the mean in rectangular variation, the correlation coefficient in bivariate normal variation, Wishart's distribution, more. 1961 edition.
This book presents a compendium of the urban layout maps of 2-mile square downtown areas of more than one hundred cities in developed and developing countries—all drawn at the same scale using high-resolution satellite images of Google Maps. The book also presents analytic studies using metric geometrical, topological (or network), and fractal measures of these maps. These analytic studies identify ordinaries, extremes, similarities, and differences in these maps; investigate the scaling properties of these maps; and develop precise descriptive categories, types and indicators for multidimensional comparative studies of these maps. The findings of these studies indicate that many geometric relations of the urban layouts of downtown areas follow regular patterns; that despite social, economic, and cultural differences among cities, the geometric measures of downtown areas in cities of developed and developing countries do not show significant differences; and that the geometric possibilities of urban layouts are vastly greater than those that have been realized so far in our cities.
Intended as a textbook for students taking a first graduate course in the subject, as well as for the general reference of interested research workers, this text discusses, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, such as robust inference and the use of the bootstrap in a multivariate setting. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear algebra.
Vorzügliches Lehrbuch über lineare Modelle für Studenten aus den Wirtschaftswissenschaften, aber auch der Mathematik, Informatik bis hin zur Psychologie. Kaum eine statistische Theorie ist so gut geeignet, die Fülle und Tiefe statistischer Ideen und Methoden zu zeigen, wie gerade die des Linearen Modells.