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It is generally accepted that training in statistics must include some exposure to the mechanics of computational statistics. This learning guide is intended for beginners in computer-aided statistical data analysis. The prerequisites for XploRe - the statistical computing environment - are an introductory course in statistics or mathematics. The reader of this book should be familiar with basic elements of matrix algebra and the use of HTML browsers. This guide is designed to help students to XploRe their data, to learn (via data interaction) about statistical methods and to disseminate their findings via the HTML outlet. The XploRe APSS (Auto Pilot Support System) is a powerful tool for finding the appropriate statistical technique (quantlet) for the data under analysis. Homogeneous quantlets are combined in XploRe into quantlibs. The XploRe language is intuitive and users with prior experience of other sta­ tistical programs will find it easy to reproduce the examples explained in this guide. The quantlets in this guide are available on the CD-ROM as well as on the Internet. The statistical operations that the student is guided into range from basic one-dimensional data analysis to more complicated tasks such as time series analysis, multivariate graphics construction, microeconometrics, panel data analysis, etc. The guide starts with a simple data analysis of pullover sales data, then in­ troduces graphics. The graphics are interactive and cover a wide range of dis­ plays of statistical data.

Inhaltsverzeichnis

Frontmatter

First Steps

Frontmatter

1. Getting Started

Abstract
Here we show how to get started with XploRe and support you in performing your first statistical analysis. We explain how you can get help and how you can do your own quantlet programming.
Wolfgang Härdle, Sigbert Klinke, Marlene Müller

2. Descriptive Statistics

Abstract
A descriptive analysis of a given data set is typically the first part of statistical modeling and evaluation of data. In the following, we will show how the functions that come with XploRe can be used for this purpose. All routines for descriptive analysis that we present are part of the libraries XploRe (basic routines) and stats (basic statistical methods). We will not use graphical methods here. Tools for the graphical exploration of data are extensively discussed in Chapter 3.
Marlene Müller

3. Graphics

Abstract
The XploRe graphics support has different levels which are described here. The levels correspond to the ease of use for different types of users.
Sigbert Klinke

4. Regression Methods

Abstract
Simply speaking, a regression problem is a way to determine a function \(\hat m( \bullet )\) describing a functional relation \(m( \bullet )\) between a p-dimensional variable \(X = ({X_1},...,{X_p})\) and an output variable Y
$$Y = m(X) + \varepsilon $$
, where \(\varepsilon \) is a random error term.
Jörg Aßmus

5. Teachware Quantlets

Abstract
Teachware quantlets comprise a basic set of interactive, illustrative examples in introductory statistics. For the student, they provide an opportunity to understand some important basic concepts in statistics through trial and error. For the teacher, they can aid instruction by allowing the students to work independently on exploratory examples at their own pace. Additionally, with a modicum of understanding of the XploRe programming language, the teacher can modify these examples to fit his/her own preferences.
Nathaniel Derby

Statistical Libraries

Frontmatter

6. Smoothing Methods

Abstract
Nonparametric smoothing methods serve several needs in statistical data analysis: They provide a flexible analysis tool, often based on interactive graphical data representation. Also, they help in constructing a model from observations, for example by graphical comparison with already existing models.
Marlene Müller

7. Generalized Linear Models

Abstract
McCullagh and Nelder (1989) summarized many approaches to relax the distributional assumptions of the classical linear model under the common term Generalized Linear Models (GLM). A generalized linear model (GLM) is a regression model of the form
$$EY = G({x^T}\beta ),$$
where EY denotes the expected value of the dependent variable Y, x is a vector of explanatory variables, β an unknown parameter vector and G(•) a known link function.
Marlene Müller

8. Neural Networks

Abstract
A neural network consists of many simple processing units that are connected by communication channels. Much of the inspiration for the field of neural networks came from the desire to perform artificial systems capable of sophisticated, perhaps intelligent computations similar to those of the human brain.
Wolfgang Härdle, Heiko Lehmann

9. Time Series

Abstract
The purpose of this chapter is to show how XploRe may be used by practitioners for analyzing observed time series. Some of the time series tools are standard in the literature. The more elaborated nonlinearity tests based on artificial neural networks are implemented for the nonadvanced use.
Petr Franěk, Wolfgang Härdle

10. Kalman Filtering

Abstract
In recursive methods the construction of an estimate at time t is based on an estimate from the previous time and the observations available in the time t. Exponential smoothing and Yule-Walker equations are examples of recursive algorithms but by defining a state-space model one can build a unifying theory of recursive methods with the Kalman filter as a general (linear) solution of filtering, smoothing and prediction problems.
Petr Franěk

11. Finance

Abstract
There is growing interest in quantifying and simulating economic processes, particularly in the statistical analysis of the behavior of financial markets. The library finance is designed for this purpose. This chapter explains and illustrates the use of XploRe for theory and practice in this setting.
Stefan Sperlich, Wolfgang Härdle

12. Microeconometrics and Panel Data

Abstract
This chapter introduces the tools available in XploRe for analyzing microdata, i.e. data sets consisting of observations on N individual units, such as persons, households or firms.
Jörg Breitung, Axel Werwatz

13. Extreme Value Analysis

Abstract
The extreme (upper or lower) parts of a sample, such as
  • flood discharges;
  • high concentration of air pollutants;
  • claim sizes over a higher priority in reinsurance business;
  • larger losses on financial markets;
have exhibited an increasing risk potential during the last decades. This is the reason why the statistical analysis of extremes has become an important question in theory and practice.
Rolf-Dieter Reiss, Michael Thomas

14. Wavelets

Abstract
Wavelets are a powerful statistical tool which can be used for a wide range of applications, namely
  • describing a signal, nonparametic estimation
  • parsimonious (approximate) representation, data compression
  • smoothing and image denoising
  • jump detection and test procedures.
One of the main advantages of wavelets is that they offer a simultaneous localization in time and frequency domain. The second main advantage of wavelets is that, using fast wavelet transform, it is computationally very fast.
Yuri Golubev, Wolfgang Härdle, Zdeněk Hlávka, Sigbert Klinke, Michael H. Neumann, Stefan Sperlich

Programming

Frontmatter

15. Reading and Writing Data

Abstract
This chapter describes the use of XploRe’s commands for reading and writing data files as well as how to set the output format for the output window. Section 15.1 introduces reading and writing simple ASCII data sets. Section 15.2 explains the input format strings which can be used to read arbitrary ASCII data files. Section 15.3 explains the format strings which can be used to write formatted numeric data. Finally, the last Section 15.4 explains how to customize the output window of XploRe.
Sigbert Klinke, Jürgen Symanzik, Marlene Müller

16. Matrix Handling

Abstract
XploRe offers a large variety of commands and tools for creating and manipulating multidimensional objects called matrices and lists. The first part of this chapter presents the basic instructions for matrix handling. The second part illustrates some topics in matrix algebra with XploRe. The last part of this chapter presents the list object, which is a useful tool for handling data sets of heterogeneous formats (e.g. text and numeric).
Yasemin Boztug, Marlene Müller

17. Quantlets and Quantlibs

Abstract
Quantlets are quantitative procedures that are designed in the XploRe language and run inside the XploRe computing environment. They may be made public on the Internet via an HTML outlet. If several quantlets serve a common aim and constitute a group of homogeneous code, they may be combined into a set of quantlets to constitute a so-called quantlib. XploRe has several such quantlibs, e.g. the collection of time series routines (quantlib times) and the smoothing methods (quantlib smoother).
Wolfgang Härdle, Zdeněk Hlávka, Sigbert Klinke

Backmatter

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