The 4th Workshop on Goodness-of-fit, Change-Point and Related Problems was held at the Department of Economics and Management of the University of Trento, 6-8 September 2019. The workshop followed similar meetings in Sevilla (2012), Athens (2015) and Bad Herrenalb (2017), and now it has become an established tradition of reviewing modern developments of the relevant statistical theory and applications as well as of attracting talented researchers of all ages. A Special Issue of the *Scandinavian Journal of Statistics* published as issue 48:2 in June 2021 contains a collection of papers presented at the event.

The workshop was also an occasion for a formal tribute to **Marie Huskova** and **Winfried Stute** in recognition of their leadership and significant contributions to statistical theory.

We present an interview between Winfried Stute and Li Xing Zhu, where Prof. Dr Stute talks about his life and career.

** Interviewer:** Li Xing Zhu (Beijing)

**Summary:** Winfried Stute studied mathematics and economics at the University of Bochum, the Federal Republic of Germany, from 1968 to 1973. He got his PhD in 1975. In 1978 he moved to the University of Munich where he habilitated in 1980. From 1981 to 1983 he was an Associate Professor in Siegen (FRG). Since 1983 he held a full professorship at Justus Liebig University of Giessen (FRG). W. Stute retired in 2012 but due to a special agreement with the university he stayed until 2018. For one year he held a chair of excellence at Carlos 3 in Madrid. W. Stute became a fellow of the Institute of Mathematical Statistics in 1990. In 2008 he received the honorary doctorate degree from the University of Santiago de Compostela. His main research was on stochastic processes and their applications in statistics. Special emphasis was on empirical processes, survival analysis, model checking and micro economics (market research).

**LXZ:** Winfried, it’s nice to talk to you again, after so many years. It seems you plan to take us on a tour. Where are we moving?

**WS:** Yes, when you are getting older, you may take some moments to look back and find out some major moves in your life, both geographically and by profession.

**LXZ:** So, let’s start with your early years. When did your interest in mathematics start?

**WS:** I was born on 20 November 1946, in a city called Bochum, Federal Republic of Germany. Bochum is located in the so-called Ruhr area, which traditionally was the industrial heart of the country. My grandfathers were a carpenter working in a coal mine and a shoemaker. What could make more fun to a small boy than “assisting” him in his workshop, with thousands of nails, lots of hammers and different kinds of glue. Otherwise, natural playgrounds were the roads with much less cars than today and the ruins left over from the war. In the first years, I developed some “emotional distance” to authorities in white, like dentists, drugstore employees or nuns running my kinder garden. This is why I escaped on the first day. My parents had no academic background. My father was a manager in the furniture business. From time to time, I was allowed to accompany the truck drivers when they delivered the furniture to the customers. Even today, when I enter a furniture shop, the special smell immediately brings my memories back. The first day at school was a disaster. Not because of authorities dressed in white but because of my mother’s idea to dress me like a pseudo-Bavarian.

**LXZ:** How was your time at school?

**WS:** In the primary school I had no problems. The next natural step was, after four years, to enter high school. Since my parents had no experience with high schools, and in order to protect their only child, I stayed one more year at the primary school. For the same reason, neglecting the advice of my teachers, in my sixth year, I entered a secondary rather than a high school. When I was eight years old some more changes took place. Since my father planned to make a career in his job, he started to move from one company to another, every two years on average. Moving to other cities implied, of course, losing good friends. Also new schools usually offered different programs which required extra efforts to fill gaps. That worked pretty well. In mathematics, after refreshing unknown stuff, I was better than the rest. Also, it showed me that I could be successful without the assistance of tutors. But moving around cost a lot of energy. The final move to a high school brought me back to Bochum. These three years were hard. Teachers in, e.g., history and geography asked us to learn the stuff by heart, which I did not like but had to accept. Mathematics was different. I did not learn anything by heart. To understand things was crucial, and this caused no problem. Luckily my teachers in math all knew what they were talking about.

First day at school (1953)

**LXZ:** What was your first contact to the university?

**WS:** The university of Bochum was, like many others in the area, founded in the middle of the 1960s. The main political idea behind that was to offer studies also to people like me, i.e., to people from the working class. In my last year at school, I attended an event offered by the newly founded institute of mathematics. Everybody who had found interest in math was invited to come and ask for information. And several hundreds of young people came. A professor was there, gave a short talk and then answered questions. One of us asked him about a possible title for a master thesis in mathematics. I remember his reply contained the name Markov. What I remember better was the reaction of the people: a big laughter. I was not irritated. When I came home, I told my parents that my decision was clear: I wanted to become a mathematician. Their comment made clear that nothing in the world would help me if I failed: you should know what you are doing.

**LXZ:** Becoming a student in mathematics typically causes a cultural shock if you compare style and level with that from school. How did you survive?

**WS:** In those years it was obligated for young men to serve in the army before entering the university. For most people this was not very popular while for me it was a possibility to have a break in my “learning cycle”. On 3 January 1967, I became a soldier. I did not want to make a career. Rather I wanted to do some practical work. At the end I became a truck driver. This job required some technical skills and knowledge, something I did not have but learned over time. In the summer of 1968, I finished my service and became a student at the University of Bochum, with a major in mathematics and a minor in economics. In the first semester starting in October 1968, I attended classes in calculus and linear algebra. I realized that the professor in calculus was the same person who had informed us three years ago. We were 300 in the class which indicates that at that time mathematics was very popular. Six months later only 100 were left. What had happened was that we had a manuscript which was not easy to digest. Actually one monograph which was recommended to us was the book by Dieudonne, a famous French mathematician who was one founder of the Bourbaki group. This group had suggested to teach and present mathematics in the most abstract and concise way. Apparently, our professor had been infected by these ideas. Only the superstars among us could scope with this. To survive I bought a book written and published pre-war. Of course, in this book one could not find heavy measure theory on non-metrizable topological spaces, but could see how things looked like on the real line. Though classes were demanding I stayed with him in the sense that I attended his classes also on deeper topological measure theory. So I became familiar with weak convergence, tightness and Portmanteau. Though we had no major applications, it was customary to look at a measure as a point in the (topological) space of all measures and develop some feeling of distance between two measures.

**LXZ:** Topological measure theory is pretty far away from statistics. When did this move happen?

**WS:** In 1970/71 things changed a bit. The institute had opened a new professorship in probability and statistics. The number one candidate was Peter Gänssler, a young docent from Cologne. He had studied in Heidelberg and got the PhD under K. Krickeberg, then proceeded to Cologne to join J. Pfanzagl’s group. Gänssler was also interested in topological measure theory, but his classes and seminars were based on the landmark book *Convergence of Probability Measures* by P. Billingsley. In particular, he discussed with us the invariance principles of Donsker. For a person who had his roots in topological measure theory, Billingsley’s book should become the most influential monograph.

**LXZ:** What were other basic concepts in Gänssler’s lectures?

Coffee time at Bochum Institute, with Prof. Gänssler in the middle (1975)

**WS:** Also, we discussed martingales. Most of it was in discrete time. The Doob-Meyer decomposition was derived in discrete time, but without discussing possible interpretations and applications. Also he gave a class in parametric statistics (maximum likelihood for classes of exponential families). The word “regression” was not mentioned. In my classes on econometrics, people were talking about beta and the linear model, without proofs. At that time, it was not clear to me, that the beta was just one way to model a function which I had understood very well, namely the factorization of a conditional expectation. To summarize, most of my classes in Bochum dealt with pure mathematics on a very high level. We were free to attend classes in other fields. So I worked a lot in algebra and functional analysis. My master thesis was completed at the end of 1972. It was on an extension of the Glivenko-Cantelli Theorem and was published in the *Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete*. It was a successful step to join two major fields of my education: measure theory and large sample theory.

**LXZ:** When you got your masters, how smooth was your transition to a research position?

**WS:** I got my masters degree in January 1973 and was very lucky to get a position as a teaching and research assistant (without tenure track) in Peter Gänssler’s group. The PhD thesis was completed two years later. This work was on the so called isotropic discrepancy, the sup-distance between the true and the empirical measure taken over all convex sets. Such topics were quite popular in those years but my plan was to stop this kind of research. Rather Gänssler and I started to write a monograph on probability (in German) which was quite successful. The book of course contained the measure theoretic tools, some asymptotic (e.g., the CLT and the LIL), U-statistics, invariance principles and martingales in discrete time. After that we worked on a survey of empirical processes (the iid case) which was published as an invited paper in *Ann Prob. *

**LXZ:**Do you remember your first conference?

**WS:** In August 1977, I attended my first conference abroad. It took place in Enschede, the Netherlands. I remember this conference mainly for three reasons. First it was the week when Elvis Presley died. Second, because I attended a talk given by the famous Professor Dynkin, a name which I knew since my early classes in measure theory. Finally, I met an attendant I have never met again but whom I remember for his question. He asked me whether I was a mathematician or a statistician. I don’t remember my precise reply but for me it was clear that the statistics I knew was just a small subarea of mathematics. But things should change soon in Bochum. A new professorship in statistics was advertised, and when the top candidate gave his first class, I had to support him as a teaching assistant. His class-notes were completely new to me and my performance must have been terrible. Maybe also because his notes

looked like a cooking book with full of recipes something I was not used to.

**LXZ:** What was the next move?

**WS:** The year 1978 brought a bigger change. Professor Gänssler had got an offer from the University of Munich which he accepted.

In the German university system, it was obligated to complete another degree, the so-called Habilitation, before one could apply for a professorship elsewhere. So, there was no question about it. We followed him and continued our cooperation in Munich. Who are we?

First my family, my wife, Gerti, and our two children, Petra and Volker. Then one of our master students, who was to become an assistant in Munich, Erich Haeusler. Finally, a young researcher from Australia who visited us for a couple of months: David Pollard. Few years later we had another visitor, Jon Wellner. They were all members of the so-called Vapnik Chervonenkis group, who studied empirical processes indexed by large classes of sets or functions.

With Jon Wellner in the Seattle mountain area (1990)

I did not join them because my major problem was to find an interesting research subject for my Habilitation. Since my statistical background was still weak, I decided to go back to my roots. This was tightness of stochastic processes, in particular empiricals. What I knew very well were the fundamental exponential bounds due to Dvoretzky, Kiefer and Wolfowitz (DKW). This was the work having the most impact on me. I admired their ingenious arguments both in the univariate and in the multivariate case. But these were global stuff. Tightness is something local. So my plan was to do something locally similar to DKW in the global setup. I began to give talks on the “global and local behavior of empirical processes”. At the same time, I continued to read papers on different topics in statistics. There were many papers on nonparametric estimation of densities. Some of them studied the sup distance. Their main tool was DKW. This looked strange to me because my slogan had already become: to study something locally one should use local tools. These things appeared in 1982, still in *Annals of Probability*. My Habilitation was completed in early 1980. Referees were P. Gänssler, R. Pyke and P. Revesz. My first class I gave as a teacher in Munich was on statistics. I had realized that somehow similar to my time at school I was on the move again. starting with measure theory through probability to maybe real life. But this time I liked it.

**LXZ:** And then you moved again?

**WS:** The 1980s brought several changes. In research I further exploited my local results (for multivariate empirical processes) in new areas. E.g., since regression is a simple linear functional of the conditional distribution, I started with local resp. conditional empirical processes. Invariance principles of Donsker could be derived in the conditional setting and then applied to smooth functionals. Another new area of research were conditional U-statistics. This in turn could be applied to what I called multi-sample classification. Conditional empirical processes could also be decomposed in their principal components and allowed for a new adaptive choice of the bandwidth. Another application was on nonparametric copula processes. Some of these issues appeared in a booklet with P. Gänssler published by Birkhäuser. Summarizing, in the 1980s. I began to improve my statistical understanding and at the same time applied my oscillation stuff to new interesting quantities. This moving around also took place in a geographic sense. Since my position in Munich was without tenure track I had to look for another position elsewhere. At the end of the 1970s I got an offer from the University of Siegen. I became a colleague of R. D. Reiss who was well known for his research on order statistics, extremes and point processes. Also M. Falk was there whom I knew from my time in Bochum and who later became a professor in Würzburg. The atmosphere at the institute was inspiring and friendly. Since my family was still in Munich, I commuted a lot between Munich and Siegen.

**LXZ:** Your final move was to Giessen.

**WS:** In 1983 the University of Giessen offered me a full professorship. After one more year of travelling the family finally came in early 1984. Giessen University was founded in 1607 and the Mathematical Institute was established in the 1870s. The university is named after Justus von Liebig, a chemist who in the nineteenth century had invented fertilizer. He was invited to England to give talks. As a consequence of his message the experimental station of Rothamsted, where Fisher has started his career, was established.

**LXZ:** When did statistics come to Giessen?

**WS:** Probability and statistics came to Giessen only in the 1970s. The first professors were G. Neuhaus who later went to Hamburg and H. Strasser, an Austrian who finally went back to Vienna. When I came in 1983, my colleague was G. Pflug, who was well known for his research in stochastic optimization. Since in the mid 1980s my private travel problems had been settled, I found more time for international conferences. The first visit to UC Davis was very illuminating since the probability and the statistics groups were in separate departments. I began to understand what in 1977 the man had in mind when he asked me about my status. My hosts in Davis were J. L. Wang and H. G. Mueller. Especially the cooperation with Jane Ling should again move my interests into new directions.

Mrs and Mr Stute in Munich (1980)

**LXZ:** The 1980s also brought you to Spain.

**WS:** In the mid-1980s I attended a conference in Bilbao, Basque country, Spain. After my talk a young man approached me and we found out that we had common scientific interests. His name was Wenceslao Gonzalez Manteiga, and it was the beginning of a lifelong friendship. Since then I visited Santiago de Compostela once a year to give weekly seminars and workshops. Because he was linked to many other Spanish colleagues I step by step became a partner of the whole north west coast (Bilbao, Santander, La Coruna, Santiago, Vigo), not to forget M. Delgado in Madrid. In 2008 I became a member of their (scientific) family.

**LXZ:** In the 1990s you came to survival analysis.

**WS:** In the 1980s a hot topic in statistics, especially among Anglo-American and Scandinavian researchers, was survival analysis. A particular feature of survival data is a kind of censorship. In other words, rather than observing the data of interest there may be a mechanism which disturbs the data. One of the best studied situations is right censorship. The simple empirical distribution is no longer available and needs to be replaced by the Kaplan–Meier estimator. For KM, the classical weights 1/*n* then become weights which typically differ from datum to datum and are random. They may be computed by applying the product limit formula to the cumulative hazard function.

Becoming a member of the Galician family, with W. G. Manteiga on the right (2008)

This function turned out to be more accessible than the distribution function when data are left or right censored. This approach created, however, major problems when one is interested in general linear or quadratic statistics, like expectations or variances. When J. L. Wang visited me in 1990 our plan was to extend the classical strong law of large numbers to data censored from the right. Among the different proofs of the SLLN there is one due to Etemadi which uses the fact that sample means form a reverse martingale. The martingale convergence theorem together with the 0–1 law then immediately yield the SLLN. Under censorship this approach does not work anymore. Actually, due to a bias, the martingale property gets lost. But what could be done was to show that Kaplan Meier integrals can be decomposed into a reverse super and a sub-martingale. A few years later I studied the central limit theorem and some quadratic statistics under censorship. Another demanding situation comes up when data are truncated. The relevant estimator was due to Lynden Bell. It has direct applications in the analysis of HIV data.

**LXZ:** Now we are approaching the time when we worked together.

**W**S: In the mid-1990s I began to work on a new manuscript for my class in Giessen. The subject was on stochastic processes and their applications to statistics. I discussed global, i.e., integrated processes versus local processes, which typically incorporated some smoothing. I talked about ill-posed problems and filtering. When I came to regression it seemed to me that there was no regression type analogue to the empirical distribution. This was the moment when I started my work on what I called integrated regression. The first contribution appeared in *Ann. Statist.* (1997). In the late 1990s we had two prominent visitors, H. Koul and L.X. Zhu. They were aware of the many parametric and semiparametric models in regression and time series analysis.

With Li Xing Zhu at Giessen Institute (1996).

Through this cooperation we were able to develop many new model check respective testing procedures also in a time series context.

**LXZ:** But then you disappeared for a couple of years.

**WS:** At our institute it was a tradition to open the winter semester

with a welcome party for the students. For this we invited a former student who should give a talk with details about the career in industry. In 1998 it was an attractive lady who had been very successful in the banking sector. The following day a couple of students who had attended the talk came to my office and “encouraged” me to offer classes in finance. I always liked students who were curious about new things. So, I agreed to elaborate a program in this field which was new to me. It should not only consist of mathematics, but also discuss the various risks and how to eliminate them. For a statistician, it was a little strange to see that in most monographs models were still truly Gaussian while in statistics the normal distribution appeared only as a limit. So my main activity in this area was to consider models featuring effects I could observe at the market. One such phenomenon was shot noise describing a slow counter-effect coming up after a jump. What was new to me was a martingale measure, in the non-Gaussian case, with possible jumps. Also I was fascinated by the fact that in all the areas I had worked on since the 1970s martingales played different but important roles.

**LXZ:** Finally you came back to statistics.

**WS:** Finance was not my last area of research. Another change of interest took place when in the early 2000s I got a telephone call from a former student of mine. He had made a career in the market research sector. Their clients had a couple of questions they were not able to analyse with the existing statistical machinery. Most of the questions were micro-economic in that they wanted to know, e.g., how a household reacts to promotion or saturation. We started to work on (a sample) of self-exciting point processes with very general compensators. They were allowed to be semi-parametric since applicants preferred parameters which were easy to interpret and triggering processes (like promotion or advertisements) which generate some shot noise effect. Standard point processes do not allow for such features. One of the co-workers from industry, K. Kopperschmidt, became my PhD student. Before we started endless discussions on a possible model, we needed some mathematics to guarantee that our estimator works if the model is true. An observation is the fact that the difference between the point process (of purchase times) minus the compensator is a martingale. While in probability theory authors have the tendency to use the word ‘observable` or predictable to describe the compensator this is not so in practical situations. Hence the mathematical part also needed some extra work. Overall studying these self-exciting phenomena gave me another chance to study martingales, but with a statistical component. Martingales were also involved when I started to study statistical questions on glass ceiling effects, a topic which was brought to me by E. Ferreira from Bilbao. When I retired in 2012, it was the right moment to remember and possibly answer the question from 1977. Math or Stat? It was both, together with applications. It was amazing that empiricals and martingales, the things I knew already in the 1970s played such a great role in so many fields.

**LXZ:** What, after retirement, do your activities look like?

**WS:** After my retirement the institute had some difficulties to fill my position. So I stayed in office for another six years. In these years I continued my search of martingales in statistics. In other words, I became a martingale chaser. One example was the Ito calculus for Brownian Motion. It is standard that smooth functions of Brownian Motion and time are a martingale if the transformation satisfies a certain partial differential equation. Solving this equation is a classical problem in calculus. Now, in a statistical set up, one could do similar things, with Brownian Motion replaced by the empirical distribution or a counting process. Solving these equations gives rise to many new martingales. Some of which are nonnegative to which one-sided stopping techniques can be applied in order to get interesting boundary crossing probabilities. One year I was on leave from Giessen and visited M. Delgado at Carlos 3 in Madrid. Miguel is special in that he has an excellent technical level and at the same time knows the econometric literature very much. He brought my attention to errors in variables. This is another example when data are blurred. There is a huge literature on nonparametric estimation starting in the 1980s. Most of this work uses Fourier together with smoothing techniques. Kernel methods are usually applied in problems which are ill-posed. So I started some work to find out whether errors in variables produce ill-posedness or not. The work is still going on. I published a short paper summarizing some examples from the literature, including errors in variables, where it is more than doubtful whether classical approaches are correct. The title of the paper is bizarre and imitates a chart-topper by Led Zeppelin in the 1970s, *Stairway To Heaven*, now heaven replaced by hell. Apparently, some editors liked the paper and asked me to submit more of such critical comments.

**LXZ:** The activities in statistics in Germany improved a lot over the past decades. Can you tell us more about this?

**WS:** The German Statistical Society was founded in 1911. From the very beginning the main focus was on data collection and management, in particular in economics and sociology. For researchers who were more oriented towards a mathematical discipline the situation was very different. The first chairs in what we call stochastics were founded only in the mid 1960s. Accordingly the number of professors advising master and PhD students was small. In West Germany they formed an informal group who met once in a year in the Mathematical Research Institute Oberwolfach. Only scientists who had received the Habilitation degree were admitted. In the late 1980s I became the speaker of this group. Also, politically, the reunification of the country took place so that it was time to open the group and make it accessible to young researchers. The first reaction to this initiative was positive. But it was pointed out to me that some connection to the German Mathematical Society would be preferred. What came out was the foundation of an independent sub-group (Fachgruppe). The first conference took place in September 1993. Since then a conference is organized every 2 years. Conference language is English. What makes me happy is that in almost 30 years there were always young colleagues pushing our field forward.

**LXZ:** How in your country are young researchers supported?

**WS:** Before we come to research, let’s talk about the study. What maybe is not known abroad is the fact that the study in Germany is free of charge. For young researchers there is a variety of possibilities to get funded. The classical way is the position of a teaching assistant. Since those positions are limited, universities also offer grants. When you apply for such a grant you should have an advisor from the university supporting your application. There are many other foundations linked to political parties or churches who sponsor young researchers or central funds, like the German Science Foundation (DFG) or the German Academic Exchange Service (DAAD). As to probability and statistics I recommend, however, the homepage of the above mentioned Fachgruppe (fg-stochastik.de).

**LXZ:** Winfried, many thanks for your time.

Images provided courtesy of Prof Dr Winfried Stute