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This textbook on computational statistics presents tools and concepts of univariate and multivariate statistical data analysis with a strong focus on applications and implementations in the statistical software R. It covers mathematical, statistical as well as programming problems in computational statistics and contains a wide variety of practical examples. In addition to the numerous R sniplets presented in the text, all computer programs (quantlets) and data sets to the book are available on GitHub and referred to in the book. This enables the reader to fully reproduce as well as modify and adjust all examples to their needs.

The book is intended for advanced undergraduate and first-year graduate students as well as for data analysts new to the job who would like a tour of the various statistical tools in a data analysis workshop. The experienced reader with a good knowledge of statistics and programming might skip some sections on univariate models and enjoy the various ma

thematical roots of multivariate techniques.

The Quantlet platform quantlet.de, quantlet.com, quantlet.org is an integrated QuantNet environment consisting of different types of statistics-related documents and program codes. Its goal is to promote reproducibility and offer a platform for sharing validated knowledge native to the social web. QuantNet and the corresponding Data-Driven Documents-based visualization allows readers to reproduce the tables, pictures and calculations inside this Springer book.

### Chapter 1. The Basics of R

Abstract
The R software package is a powerful and flexible tool for statistical analysis which is used by practitioners and researchers alike. A basic understanding of R allows applying a wide variety of statistical methods to actual data and presenting the results clearly and understandably. This chapter provides help in setting up the programme and gives a brief introduction to its basics.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 2. Numerical Techniques

Abstract
With more and more practical problems of applied mathematics appearing in different disciplines, such as chemistry, biology, geology, management and economics, to mention just a few, the demand for numerical computation has considerably increased. These problems frequently have no analytical solution or the exact result is time-consuming to derive. To solve these problems, numerical techniques are used to approximate the result. This chapter introduces matrix algebra, numerical integration, differentiation and root finding.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 3. Combinatorics and Discrete Distributions

Abstract
In the second half of the nineteenth century, the German mathematician Georg Cantor developed the greater part of today’s set theory.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 4. Univariate Distributions

Abstract
In this chapter, the theory of discrete random variables from Chap. 3 is extended to continuous random variables. At first, we give an introduction to the basic definitions and properties of continuous distributions in general. Then we elaborate on the normal distribution and its key role in statistics. Finally, we exposit in detail several other key distributions, such as the exponential and $$\chi ^2$$ distributions.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 5. Univariate Statistical Analysis

Abstract
This chapter presents basic statistical methods used in describing and analysing univariate data in R. It covers the topics of descriptive and inferential statistics of univariate data, which are mostly treated in introductory courses in Statistics.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 6. Multivariate Distributions

Abstract
The preceding chapters discussed the behaviour of a single rv. This chapter introduces the basic tools of statistics and probability theory for multivariate analysis, where the relations between d rvs are considered
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 7. Regression Models

Abstract
Regression models are extremely important in describing relationships between variables. Linear regression is a simple, but powerful tool in investigating linear dependencies. It relies, however, on strict distributional assumptions. Nonparametric regression models are widely used, because fewer assumptions about the data at hand are necessary.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 8. Multivariate Statistical Analysis

Abstract
Multivariate procedures are at present widely used in finance, marketing, medicine and many other fields of theoretical and empirical research. This chapter introduces the basic tools of multivariate statistics in R.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 9. Random Numbers in R

Abstract
Random number generation has many applications in economic, statistical, and financial problems. With the advantage of high speed and cheap computation, new statistical methods using random number generation have been developed. Important examples are the bootstrap based procedures.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin

### Chapter 10. Advanced Graphical Techniques in R

Abstract
Data visualisation is an important part of data analysis with R. The standard Renvironment has various graphical facilities for drawing different types of statistical plots. However, there exist several shortcuts not covered in the base Rgraphical system.
Wolfgang Karl Härdle, Ostap Okhrin, Yarema Okhrin