W. Gurker:

"Introduction to Mathematical Statistics using R";

TU-MV Media Verlag GmbH, Wien, 2018, ISBN: 9783903024809; 554 S.

Introduction to Mathematical Statistics using R

This is a text for beginning students of statistics who would like to understand the theory behindsome of the most common statistical procedures used in applications. Emphasis is laid on themathematical but also on the computational aspects of statistics. Throughout we make use of the statistical software R and provide working R-code for the examples in the text and for some of the problems. (The data sets and R-scripts can be downloaded from the website of the TUVerlag.)

In Sections 1 to 6 we discuss the fundamentals of probability theory as far as they are needed in statistics. Beginning with Section 7 we introduce the framework of statistical modeling and inference, mainly from a classical but also from a Bayesian perspective.

Apart from various empirical and graphical procedures, we discuss the basics of estimation and hypothesis testing, methods for constructing confidence intervals and some methods of nonparametric statistical inference. Likelihood methods which are central in parametric statistical inference, are discussed in some detail. However, we also touch on some more advanced topics such as sufficiency, and discuss numerical and simulation techniques such as the EM algorithm and MCMC methods. We conclude with a section on linear models, in particular linear regression and ANOVA models.

The main topics are:

Probability Models - Random Variables - Bivariate Random Vectors - Multivariate Distributions

- Some Special Distributions - Limit Theorems - Sample Statistics - Statistical Inference -

Likelihood Methods - Bayesian Inference - Nonparametric Procedures - Linear Models

Probability Models, Random Variables, Multivariate Distributions, Sample Statistics

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.