The Theory of Dispersion Models


Book Description

The theory of dispersion models straddles both statistics and probability, and involves an encyclopedic collection of tools, such as exponential families, asymptotic theory, stochastic processes, Tauber theory, infinite divisibility, and stable distributions. The Theory of Dispersion Models introduces the reader to these models, which serve as error distributions for generalized linear models, and looks at their applications within this context.




An Introduction to Bartlett Correction and Bias Reduction


Book Description

This book presents a concise introduction to Bartlett and Bartlett-type corrections of statistical tests and bias correction of point estimators. The underlying idea behind both groups of corrections is to obtain higher accuracy in small samples. While the main focus is on corrections that can be analytically derived, the authors also present alternative strategies for improving estimators and tests based on bootstrap, a data resampling technique and discuss concrete applications to several important statistical models.




Evaluation of Information in Longitudinal Data


Book Description

"This is a Ph.D. dissertation. Longitudinal analysis is important when individual effects are present. In this thesis some methods for different kinds of inference on longitudinal data are derived and evaluated in small sample settings. Appropriate evaluation criteria are determined from the actual inferential situation. It is based on three papers: ""Maximum Likelihood Ratio Based Small-Sample Tests for Random Coefficients in Linear Regression"", ""Preliminary Testing in a Class of Simple Non-Linear Mixed Models to Improve Estimation Accuracy"" and ""Detection of Intra-Uterine Growth Restriction""."







Exponential Family Nonlinear Models


Book Description

This book gives a comprehensive introduction to exponential family nonlinear models, which are the natural extension of generalized linear models and normal nonlinear regression models. The differential geometric framework is presented for these models and geometric methods are widely used in this book. This book is ideally suited for researchers in statistical interfaces and graduate students with a basic knowledge of statistics.










Data Science for Business and Decision Making


Book Description

Data Science for Business and Decision Making covers both statistics and operations research while most competing textbooks focus on one or the other. As a result, the book more clearly defines the principles of business analytics for those who want to apply quantitative methods in their work. Its emphasis reflects the importance of regression, optimization and simulation for practitioners of business analytics. Each chapter uses a didactic format that is followed by exercises and answers. Freely-accessible datasets enable students and professionals to work with Excel, Stata Statistical Software®, and IBM SPSS Statistics Software®. - Combines statistics and operations research modeling to teach the principles of business analytics - Written for students who want to apply statistics, optimization and multivariate modeling to gain competitive advantages in business - Shows how powerful software packages, such as SPSS and Stata, can create graphical and numerical outputs