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This book grew out of many years of involvement with the practical applications of extreme value analysis to measured or simulated data. This is a fascinating area of research because of the fundamental dichotomy inherent in this problem area. On the one hand, you have beautiful mathematical results for asymptotic extreme value distributions. On the other hand, you have real-life data, which are hardly asymptotic. So, the unavoidable question becomes: To what extent can you use the asymptotic distributions to analyze real-life data? Personally, I have always felt uncomfortable with the use of the parametric classes of asymptotic extreme value distributions in applications. This was largely due to the fact that the justification for applying them generally seemed dubious, and amazingly enough, the problem of justification is rarely discussed at all in papers using asymptotic distributions on real-life data. The problems of justification and other issues related to the fundamental dichotomy, are discussed in Chapter~\ref{chap:challenges}. 

Of course, I was not the only one who disliked asymptotics for use on real-life data. A consequence of this situation was that alternative procedures for extreme value analysis were developed in several engineering disciplines. Some of these alternative procedures were based on ideas similar to those developed in Chapter~\ref{chap:cr}. This chapter contains what was largely my world view on applied extreme value statistics for quite some time, and to some extent, it still is. However, the development of the ACER method, which is a central theme in this book, cf. Chapter~\ref{chap:acer}, allows for a much wider perspective. Its use in practice basically involves two separate steps. The first step is based exclusively on the data and ends up with a nonparametric representation of the extreme value distribution inherent in the data. This is the crucial element of the ACER method. The second step consists of an optimization procedure to fit a parametric function to the nonparametric distribution. This step is necessary in order to be able to predict extremes larger than those contained in the data, which is typically demanded by applications. To develop a rational method of optimized fitting, the asymptotic extreme value theory by necessity becomes an essential ingredient which guides the construction of the parametric functions used in the optimization procedure. It is therefore necessary to identify the correct asymptotic extreme value distribution, since the fitted extreme value distribution by necessity must approach the relevant asymptotic form in the limit. 
   

Even if my own work in developing methods for use in applied extreme value analysis more or less avoided direct use of the asymptotic extreme value distributions, I have always clearly understood their importance as an unavoidable foundation. The publication in 1983 of the important book 'Extremes and Related Properties of Random Sequences and Processes' by Leadbetter, Lindgren and Rootz\'{e}n, happened when my own interest in extreme value analysis more or less started. I, therefore, read this book very carefully, and it gave me a very good grip on the asymptotic extreme value theory. Of course, I also read parts of the seminal book by E. J. Gumbel, published in 1958, which also has a focus on asymptotic results. However, by the mid-1980s, that book, which was written in a pre-computer era, appeared as more or less obsolete when compared to the book by Leadbetter et al.  

I have written this book, not because I want to convince people to abandon the classical asymptotic approaches, which, unfortunately, too often in practice are reduced to blindfolded curve fitting exercises to asymptotic parametric distributions with no real analysis to back it up. No, I have written the book because I would also like to show that it is now possible to make a more rationally based extreme value analysis of observed data. I want to show that the ACER method very often provides a unique practical diagnostic tool for a rational extreme value analysis. If, as a result, asymptotic distributions turn out to be more or less acceptable, then their use would at least have a reasonable justification. 

It is also important to emphasize that the book is not a comprehensive treatment of methods for applied extreme value analyses, but to a large extent a collection of methods that I have personally worked with on and off over a period of three decades, and which I have found to be relevant and useful. I have made an effort to write the book as much as possible like an introduction to extreme value statistics with emphasis on applications. Therefore, the book also contains introductory chapters to the classical asymptotic theories and the threshold exceedance models, as well as many illustrative examples. The mathematical level is elementary, and detailed mathematical proofs have been avoided in favour of heuristic arguments to increase readability. Hopefully, this makes the book useful and appealing to a large audience of people representing a wide range of diverse applications. 

Since the topic of this book is applied extreme value statistics, an inevitable component to go along with it, is access to computer programs for carrying out the analysis of available data. For the methods based on the asymptotic results described in Chapters~\ref{chap:aevt} and \ref{chap:pot}, there are several excellent programs easily available. Specific recommendations are not given here. Whichever program is chosen, good results can be obtained within the framework of asymptotic distributions. On the other hand, the ACER method has not yet attained a comparable level of software development. References to computer programs for univariate and bivariate analyses by the ACER method, has therefore been given in this book. These programs can be freely downloaded. 

Writing on the technical level necessary for this book, requires a lot of attention to details. It is in practice impossible to avoid errors and mistakes, poorly formulated explanations or misprints in initial versions of such a book. Fortunately, I have some very good friends and colleagues who have helped me identify and correct many such shortcomings, and for this, I am forever thankful. Any mistakes, that may still remain, are entirely my own responsibility. The first group of people that I would like to mention for their important contributions to improving the book, are Professors Bernt J. Leira, Bo H. Lindqvist, Sverre Haver, and Dr. Karl W. Breitung. Previous collaborators and PhD students that have been important in helping me in various ways, are Professors Torgeir Moan, Oleg Gaidai, Sjur Westgaard, Marc Maes, Nilanjan Saha, Wei Chai, Arild Brandrud N{\ae}ss, and Drs. Oleksandr Batsevich, Oleh Karpa, Ali Cetin, Hans K. Karlsen, Kai Erik Dahlen, and MSc Morten Skjong. I am also very grateful to my many good students that I have had the pleasure of working with over the years, who have also inevitably been part of my own never-ending education as a researcher. 


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Trondheim, March 2023 \hfill {\it Arvid Naess}\\
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