M.Sc. (Moscow University)
Ph.D. (Russian Academy of Science)
D.Sc. (Vilnius University)
My area of expertise is Mathematical Statistics. Classical Statistics is primarily concerned with estimating unknown parameters of probability distributions, based on observations drawn from such distributions. In the early seventies, after graduating from Moscow University and obtaining my Ph.D., I became interested in statistical problems depending on infinitely many parameters. Classical notions such as efficiency and Fisher information may be carried over to situations where a description by just a finite number of parameters is no longer sufficient.
In the eighties, I became interested in the problem of how to characterize statistical estimates which are efficient not only to first order approximation, but also to the second and possibly higher order approximation. The solution to this problem, as it turned out, lies in the properties of corresponding elliptic differential operators. The use of partial Differential Equations and Differential Geometry became essential therefore in studying a problem that originally appeared purely statistical. These results led to my habilitation Theses.
After that I have lectured in the US and for the last almost ten years in Holland, at the University of Utrecht. My former students there are still working in Holland. One is Professor at the University of Leiden, another is preparing to present his Thesis by the end of this year, others are working at different research labs.
During the last 10 years I have been working jointly with my French colleagues in the area of non-parametric Statistics. This modern area of Statistics is concerned with problems in which the unknowns to be estimated may be viewed as functions, such as the response of a system to different stimuli, a transmitted signal disturbed by a noise in a communication channel, or a picture whose sharpness has deteriorated. Here again ideas from other related parts of Mathematics, such as Fourier transforms and filtering of stationary stochastic processes, prove extremely useful.
A student may ask himself: how do I decide whether Mathematical Statistics might be interesting to me? Here I would like to mention several suggestive answers highlighting different aspects of this science based on my own experience.
First, as it can be seen from the preceding, Statistics incorporates knowledge from many adjacent disciplines such as Probability Theory, Random Processes, Differential Geometry, Fourier Analysis, Approximation Theory. And it is there, on the borders between different theories, that the most exciting discoveries can be made.
Second, many statistical findings, or even hypotheses yet to be proved, can be investigated by simulating them using modern computer software. This helps to make theoretical problems much more real and often helps the researcher by either confirming or disapproving his a priory ideas.
Research Interests (Cont.d)
Finally, it is relatively easy to find applications of Mathematical Statistics in many other areas, such as Financial mathematics, Image restoration, Signal processing, Econometrics etc. To give an example, let me tell you how I have recently become interested in the Epidemiology. I was asked to assist a group of students in a project aimed at analyzing an infectious ailment which threatened farmers. livestock in Holland. The exact cause and the ways in which this ailment might spread were unclear to the experts. However, by analyzing the available data using statistical methods, the group realized that the progression of that decease could be explained by a relatively simple statistical model which then appeared universally applicable to the spread of epidemics transmitted by viruses. Using these methods it was possible to estimate the speed of spreading and predict quite accurately the end of the epidemic.
At present I am Associate Editor of the journal `Mathematical Methods of Statistics'. I am member of the following scientific societies: AMS, IMS, ISI, Bernoulli.