New methods of investigation of the limiting behavior of statistical parameter
estimates in the asymptotic estimation theory were suggested, which led to the final
solution of the old problem about the asymptotic efficiency of maximum likelihood
estimates. Methods of solution of nonparametric estimation problems were developed.
The approximation of the distributions of sums of independent random variables by
infinite divisible distributions was studied. In particular an old A.N.Kolmogorov's
problem about the order of accuracy of such approximation in the Levy metric was solved.
Methods of investigation of asymptotic behavior of the distributions of functionals
defined on random walks were suggested, which permitted to prove, for the first time,
the appropriate limit theorems under natural conditions.
Researches were carried out in the theory of Gaussian processes, spectral theory and
in statistics of stationary processes and homogeneous fields.
