Universal local constant and local linear kernel estimators in nonparametric regression. I.
In the talk we will discuss two classes of universal kernel-type estimators in nonparametric regression
uniformly consistent under close to minimal and illustrative conditions on design points.
The universality of estimators lies in the fact that their
asymptotic properties do not depend on the structure of correlation of the design elements, with respect
to which the domain of the regression function is supposed to be densely filled in some sense. Some of the results presented in the talk
are joint studies with I.S. Borisov,
P.S. Ruzankin, E.B. Yarovaya (MSU), V.A. Kutsenko (MSU), and S.A. Shalnova (National Medical Research Center for Therapy and Preventive Medicine).
New opportunities in image analysis of modern nuclear medicine
The achievements and unsolved problems of modern diagnostic nuclear medicine based on the methods of single-photon emission computed tomography (SPECT) and positron emission tomography (PET) will be reviewed. The capabilities of mathematical modeling of a patient examination by the SPECT method making use of the "virtual patient", the "virtual tomograph" and applying statistical techniques to solve the inverse problem of image reconstruction will be discussed. The promising directions of the nuclear medicine of the nearest future, including the development of theranostics and radiomics, will be discussed.