Wolfgang Härdle

This book describes an interactive statistical computing environment called 1 XploRe. As the name suggests, support for exploratory statistical analysis is given by a variety of computational tools. XploRe is a matrix-oriented statistical language with a comprehensive set of basic statistical operations that provides highly interactive graphics, as well as a programming environ­ ment for user-written macros; it offers hard-wired smoothing procedures for effective high-dimensional data analysis. Its highly dynamic graphic capa­ bilities make it possible to construct student-level front ends for teaching basic elements of statistics. Hot keys make it an easy-to-use computing environment for statistical analysis. The primary objective of this book is to show how the XploRe system can be used as an effective computing environment for a large number of statistical tasks. The computing tasks we consider range from basic data matrix manipulations to interactive customizing of graphs and dynamic fit­ ting of high-dimensional statistical models. The XploRe language is similar to other statistical languages and offers an interactive help system that can be extended to user-written algorithms. The language is intuitive and read­ ers with access to other systems can, without major difficulty, reproduce the examples presented here and use them as a basis for further investigation.

The author has attempted to present a book that provides a non-technical introduction into the area of non-parametric density and regression function estimation. The application of these methods is discussed in terms of the S computing environment. Smoothing in high dimensions faces the problem of data sparseness. A principal feature of smoothing, the averaging of data points in a prescribed neighborhood, is not really practicable in dimensions greater than three if we have just one hundred data points. Additive models provide a way out of this dilemma; but, for their interactiveness and recursiveness, they require highly effective algorithms. For this purpose, the method of WARPing (Weighted Averaging using Rounded Points) is described in great detail.

In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.

The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap­ proximation of possibly irregular functions and surfaces and was successfully applied in data compression, turbulence analysis, image and signal process­ ing. Five years ago wavelet theory progressively appeared to be a power­ ful framework for nonparametric statistical problems. Efficient computa­ tional implementations are beginning to surface in this second lustrum of the nineties. This book brings together these three main streams of wavelet theory. It presents the theory, discusses approximations and gives a variety of statistical applications. It is the aim of this text to introduce the novice in this field into the various aspects of wavelets. Wavelets require a highly interactive computing interface. We present therefore all applications with software code from an interactive statistical computing environment. Readers interested in theory and construction of wavelets will find here in a condensed form results that are somewhat scattered around in the research literature. A practioner will be able to use wavelets via the available software code. We hope therefore to address both theory and practice with this book and thus help to construct bridges between the different groups of scientists. This te. xt grew out of a French-German cooperation (Seminaire Paris­ Berlin, Seminar Berlin-Paris). This seminar brings together theoretical and applied statisticians from Berlin and Paris. This work originates in the first of these seminars organized in Garchy, Burgundy in 1994.

This book describes an interactive statistical computing environment called 1 XploRe. As the name suggests, support for exploratory statistical analysis is given by a variety of computational tools. XploRe is a matrix-oriented statistical language with a comprehensive set of basic statistical operations that provides highly interactive graphics, as well as a programming environ­ ment for user-written macros; it offers hard-wired smoothing procedures for effective high-dimensional data analysis. Its highly dynamic graphic capa­ bilities make it possible to construct student-level front ends for teaching basic elements of statistics. Hot keys make it an easy-to-use computing environment for statistical analysis. The primary objective of this book is to show how the XploRe system can be used as an effective computing environment for a large number of statistical tasks. The computing tasks we consider range from basic data matrix manipulations to interactive customizing of graphs and dynamic fit­ ting of high-dimensional statistical models. The XploRe language is similar to other statistical languages and offers an interactive help system that can be extended to user-written algorithms. The language is intuitive and read­ ers with access to other systems can, without major difficulty, reproduce the examples presented here and use them as a basis for further investigation.

Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable. The computer and the development of interactive graphics programs have made curve estimation possible. This volume focuses on the applications and practical problems of two central aspects of curve smoothing: the choice of smoothing parameters and the construction of confidence bounds. Härdle argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing. To simplify the exposition, kernel smoothers are introduced and discussed in great detail. Building on this exposition, various other smoothing methods (among them splines and orthogonal polynomials) are presented and their merits discussed. All the methods presented can be understood on an intuitive level; however, exercises and supplemental materials are provided for those readers desiring a deeper understanding of the techniques. The methods covered in this text have numerous applications in many areas using statistical analysis. Examples are drawn from economics as well as from other disciplines including medicine and engineering.

The author has attempted to present a book that provides a non-technical introduction into the area of non-parametric density and regression function estimation. The application of these methods is discussed in terms of the S computing environment. Smoothing in high dimensions faces the problem of data sparseness. A principal feature of smoothing, the averaging of data points in a prescribed neighborhood, is not really practicable in dimensions greater than three if we have just one hundred data points. Additive models provide a way out of this dilemma; but, for their interactiveness and recursiveness, they require highly effective algorithms. For this purpose, the method of WARPing (Weighted Averaging using Rounded Points) is described in great detail.

Because of the sheer size and scope of the plastics industry, the title Developments in Plastics Technology now covers an incredibly wide range of subjects or topics. No single volume can survey the whole field in any depth and what follows is, therefore, a series of chapters on selected topics. The topics were selected by us, the editors, because of their immediate relevance to the plastics industry. When one considers the advancements of the plastics processing machinery (in terms of its speed of operation and conciseness of control), it was felt that several chapters should be included which related to the types of control systems used and the correct usage of hydraulics. The importance of using cellular, rubber-modified and engineering-type plastics has had a major impact on the plastics industry and therefore a chapter on each of these subjects has been included. The two remaining chapters are on the characterisation and behaviour of polymer structures, both subjects again being of current academic or industrial interest. Each of the contributions was written by a specialist in that field and to them all, we, the editors, extend our heartfelt thanks, as writing a contribution for a book such as this, while doing a full-time job, is no easy task.