Isotonic considerations

When I started thinking about a topic for my dissertation (at a time when Ph. D. students were often still deciding on these matters themselves), I first thought of the area of isotonic regression. But then one of the Dutch professors of Statistics assured me that "the topic was dead". So, for this reason (and possibly other reasons as well), my dissertation was on probabilities of large deviations and not on isotonic regression, although I presently think that isotonic regression is a much more interesting topic. What makes isotonic regression problems so fascinating is that they arise quite naturally in lots of contexts and that, at the same time, there is usually no standard machinery available to tackle them. So, when I got my chance with my own Ph. D. students, I encouraged them to work on topics related to isotonic regression. In my lecture I will try to explain what isotonic regression is all about and I will also discuss recent work in the area.