5 papers
Asymptotically exact constants in natural convergence rate estimates in the Lindeberg theorem
Ruslan Gabdullin, Vladimir Makarenko, Irina Shevtsova
Following (Shevtsova, 2010) we introduce detailed classification of the asymptotically exact constants in natural estimates of the rate of convergence in the Lindeberg central limi…
Lower bounds for the constants in non-uniform estimates of the rate of convergence in the CLT
Irina Shevtsova
We conduct a comparative analysis of the constants in the Nagaev-Bikelis and Bikelis-Petrov inequalities which establish non-uniform estimates of the rate of convergence in the cen…
On natural convergence rate estimates in the Lindeberg theorem
Ruslan Gabdullin, Vladimir Makarenko, Irina Shevtsova
We prove two estimates of the rate of convergence in the Lindeberg theorem, involving algebraic truncated third-order moments and the classical Lindeberg fraction, which generalize…
Esseen-Rozovskii type estimates for the rate of convergence in the Lindeberg theorem
Ruslan Gabdullin, Vladimir Makarenko, Irina Shevtsova
We present structural improvements of Esseen's (1969) and Rozovskii's (1974) estimates for the rate of convergence in the Lindeberg theorem and also compute the appearing absolute…
An optimal Berry-Esseen type theorem for integrals of smooth functions
Lutz Mattner, Irina Shevtsova
We prove a Berry-Esseen type inequality for approximating expectations of sufficiently smooth functions , like , with respect to standardized convolutions of laws $…