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Leonid Sirota

Publications and source records attributed to Leonid Sirota.

27 records · Page 2Linked to original sources
arXiv2015

Grand Lebesgue norm estimation for binary random variables, with applications

We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable. This norm is optimal for the centered and bounded random variables (r.v.). Using this result we derive a very simple bilateral sharp exponential tail estimates for sums of these variables, not necessary to be identical distributed, under non-standard norming, and give some examples to show the exactness of our estimates.

math.PR↗
arXiv2014

Subgaussian and strictly subgaussian random variable

We study in this report the so-called Strictly Subgaussian (SSub) random variables (r.v.), which form a very interest subclass of Subgaussian (Sub) r.v., and obtain the exact exponential bounds for tail of distribution for sums of independent and disjoint such a variables, not necessary to be identical distributed, and give some new examples of SSub variables to show the exactness of our estimates. We extend also these results on the case of sums of subgaussian martingale differences, and show that the mixture of (Strictly) Subgaussian r.v. forms also (Strictly) subgaussian variable.

math.PR↗
arXiv2014

Exact value for subgaussian norm of centered indicator random variable

We calculate the exact subgaussian norm of a centered (shifted) indicator (Bernoulli's) random variable. Using this result we derive very simple tail estimates for sums of these variables, not necessary to be identical distributed, and give some examples to show the exactness of our estimates.

math.PR↗
arXiv2009

Bilateral Small Lebesgue Spaces

In this article we investigate the so-called Bilateral Small Lebesgue Spaces: prove that they are associated to the Grand Lebesgue spaces, calculate its fundamental functions and Boyd's indices find its dual spaces etc.

math.FA↗
arXiv2008

Optimal Adaptive Nonparametric Denoising of Multidimensional - Time Signal

We construct an adaptive asymptotically optimal in the classical norm of the space L(2) of square integrable functions non - parametrical multidimensional time defined signal regaining (adaptive filtration, noise canceller) on the background noise via multidimensional truncated Legendre expansion and optimal experience design. The two - dimensional case is known as a picture processing, picture analysis or image processing. We offer a two version of an confidence region building, also adaptive. Our estimates proposed by us have successfully passed experimental tests on problem by simulate of modeled with the use of pseudo-random numbers as well as on real data (of seismic signals etc.) for which our estimations of the different signals were compared with classical estimates obtained by the kernel or wavelets estimations method. The precision of proposed here estimations is better. Our adaptive truncation may be used also for the signal and image compression.

physics.data-an↗
arXiv2004

Universal Adaptive Estimations and Confidence Intervals in the Nonparametric Statistics

The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace compactly embedded in space $L_2$, and confidence intervals, also adaptive, are constructed on their basis for the estimated functions in an integral norm.

math.PR↗