113 citations · 228 across the 9 of their papers we have counts for
10 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…
Estimates of the accuracy of asymptotic probability models
Irina Shevtsova
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
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 $…
On the accuracy of the approximation of the complex exponent by the first terms of its Taylor expansion with applications
Irina Shevtsova
A new bound for the remainder term in the Taylor expansion of the complex exponent , , is proved yielding precise moment-type estimates of the accuracy of the appro…
A square bias transformation: properties and applications
Irina Shevtsova
The properties of the square bias transformation are studied, in particular, the precise moment-type estimate for the -metric between the transformed and the original distribu…
On the absolute constants in the Berry-Esseen type inequalities for identically distributed summands
Irina Shevtsova
By a modification of the method that was applied in (Korolev and Shevtsova, 2010), here the inequalities and $Δ_n\leq0.33554(β_3+0.415)/\sqrt{n}…
An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums
Victor Korolev, Irina Shevtsova
By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities and $$ρ(F_n,Φ)\le \frac…