Multiparametric Statistics

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

The underlying principles invented and developed by Dr. Genichi Taguchi (1924 - 2012), for the design of experiments or simulation calculations in multi-parameter systems, are today known as Taguchi Method. Due to the great success, it was extended to many other areas. The book explains the basics of this method in as much detail as necessary and as simply and graphically as possible. The author shows how broad the current application spectrum is and for which different tasks it can be used. The application examples range from optimizing a fermentation process in biotechnology to minimizing costs in mechanical production and maintaining and improving competitiveness in industrial production. The processes described are ideally suited to finding reliable and precise solutions for a wide variety of problems relatively quickly. A real competitive advantage not only in research but also for companies that want to remain competitive in international business competition. Contents Part 1: Analysis of Variables Part 2: Pattern Recognition and Diagnosis Part 3: Prognosis Target groups Students, scientists, engineers or those responsible for development and products learn to use the Taguchi Method with this book - even without any previous mathematical-statistical knowledge. The author Herbert Ruefer studied physics and obtained his doctorate at the Technical University Karlsruhe, Germany. After a research stay at IBM, San Jose, California, he taught at the San Marcos National University in Lima, Peru. He then took on research, development, and training tasks in the chemical industry in Germany. During this time, the first personal contacts with Dr. Genichi Taguchi and Dr. Yuin Wu took place. After his active professional life, he dedicated himself to special optical methods for astronomical observations. He also lectures at the Universidad Nacional Mayor de San Marcos which awarded him an honorary doctorate in 2017.

Advanced Statistics for Health Research provides a rigorous geometric understanding of models used in the analysis of health data, including linear and non-linear regression models, and supervised machine learning models. Models drawn from the health literature include: ordinary least squares, two-stage least squares, probits, logits, Cox regressions, duration modeling, quantile regression and random forest regression. Causal inference techniques from the health literature are presented including randomization, matching and propensity score matching, differences-in-differences, instrumental variables, regression discontinuity, and fixed effects analysis. Codes for the respective statistical techniques presented are given for STATA, SAS and R.

This landmark text from world-leading radiologist describes and illustrates how imaging techniques are created, analyzed and applied to biomedical problems.

Topic Editor MS received funding from Bayer AG.

An Introduction to Nonparametric Statistics presents techniques for statistical analysis in the absence of strong assumptions about the distributions generating the data. Rank-based and resampling techniques are heavily represented, but robust techniques are considered as well. These techniques include one-sample testing and estimation, multi-sample testing and estimation, and regression. Attention is paid to the intellectual development of the field, with a thorough review of bibliographical references. Computational tools, in R and SAS, are developed and illustrated via examples. Exercises designed to reinforce examples are included. Features Rank-based techniques including sign, Kruskal-Wallis, Friedman, Mann-Whitney and Wilcoxon tests are presented Tests are inverted to produce estimates and confidence intervals Multivariate tests are explored Techniques reflecting the dependence of a response variable on explanatory variables are presented Density estimation is explored The bootstrap and jackknife are discussed This text is intended for a graduate student in applied statistics. The course is best taken after an introductory course in statistical methodology, elementary probability, and regression. Mathematical prerequisites include calculus through multivariate differentiation and integration, and, ideally, a course in matrix algebra.

2004 BMA Medical Book Competition Winner (Radiology category) “This is an exciting book, with a new approach to use of the MRI scanner. It bridges the gap between clinical research and general neuro-radiological practice. It is accessible to the clinical radiologist, and yet thorough in its treatment of the underlying physics and of the science of measurement. It is likely to become a classic.” British Medical Association This indispensable 'how to' manual of quantitative MR is essential for anyone who wants to use the gamut of modern quantitative methods to measure the effects of neurological disease, its progression, and its response to treatment. It contains both the methodology and clinical applications, reflecting the increasing interest in quantitative MR in studying disease and its progression. The editor is an MR scientist with an international reputation for high quality research The contributions are written jointly by MR physicists and MR clinicians, producing a practical book for both the research and medical communities A practical book for both the research and medical communities “Paul Tofts has succeeded brilliantly in capturing the essence of what needs to become the future of radiology in particular, and medicine in general – quantitative measurements of disease.” Robert I. Grossman, M.D. New York, University School of Medicine (from the Foreword)