arXiv subjects
Publications and source records attributed to D. O. Ivanenko.
The article considers vector parameter estimators in statistical models generated by Levy processes. An improved one step estimator is presented that can be used for improving any other estimator. Combined numerical methods for optimization problems are proposed. A software has been developed and a correspondent testing and comparison have been presented.
By means of the Malliavin calculus, integral representation for the second derivative of the loglikelihood function are given for a model based on discrete time observations of the solution to SDE driven by a Levy process.
By means of the Malliavin calculus, integral representations for the likelihood function and for the derivative of the log-likelihood function are given for a model based on discrete time observations of the solution to equation dX_t=a_θ(X_t)dt + dZ_t with a tempered α-stable process Z. Using these representations, regularity of the statistical experiment and the Cramer-Rao inequality are proved.