V.I. Serdobolskii – författare
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2 produkter
2 produkter
Del 41 - Theory and Decision Library B
Multivariate Statistical Analysis
A High-Dimensional Approach
Inbunden, Engelska, 2000
1 082 kr
Skickas inom 10-15 vardagar
Presents a new branch of mathematical statistics aimed at constructing unimprovable methods of multivariate analysis, multi-parametric estimation, and discriminant and regression analysis. In contrast to the traditional consistent Fisher method of statistics, the essentially multivariate technique is based on the decision function approach by A. Wald. Developing this new method for high dimensions, comparable in magnitude with sample size, provides stable approximately unimprovable procedures in some wide classes, depending on an arbitrary function. A fact is established that, for high-dimensional problems, under some weak restrictions on the variable dependence, the standard quality functions of regularized multivariate procedures prove to be independent of distributions. This opens the possibility to construct unimprovable procedures free from distributions.
Del 41 - Theory and Decision Library B
Multivariate Statistical Analysis
A High-Dimensional Approach
Häftad, Engelska, 2010
1 073 kr
Skickas inom 10-15 vardagar
In the last few decades the accumulation of large amounts of in formation in numerous applications. has stimtllated an increased in terest in multivariate analysis. Computer technologies allow one to use multi-dimensional and multi-parametric models successfully. At the same time, an interest arose in statistical analysis with a de ficiency of sample data. Nevertheless, it is difficult to describe the recent state of affairs in applied multivariate methods as satisfactory. Unimprovable (dominating) statistical procedures are still unknown except for a few specific cases. The simplest problem of estimat ing the mean vector with minimum quadratic risk is unsolved, even for normal distributions. Commonly used standard linear multivari ate procedures based on the inversion of sample covariance matrices can lead to unstable results or provide no solution in dependence of data. Programs included in standard statistical packages cannot process 'multi-collinear data' and there are no theoretical recommen dations except to ignore a part of the data. The probability of data degeneration increases with the dimension n, and for n > N, where N is the sample size, the sample covariance matrix has no inverse. Thus nearly all conventional linear methods of multivariate statis tics prove to be unreliable or even not applicable to high-dimensional data.