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Of all publications in the section: 7
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Article
Philip Dawid A., Shafer G., Shen A. et al. Statistics and Probability Letters. 2011. Vol. 81. No. 1. P. 157-162.

Statistical testing can be framed as a repetitive game between two players, Forecaster and Sceptic. On each round, Forecaster sets prices for various gambles, and Sceptic chooses which gambles to make. If Sceptic multiplies by a large factor the capital he puts at risk, he has evidence against Forecaster’s ability. His capital at the end of each round is a measure of his evidence against Forecaster so far. This can go up and then back down. If you report the maximum so far instead of the current value, you are exaggerating the evidence against Forecaster. In this article, we show how to remove the exaggeration. Removing it means systematically reducing the maximum in such a way that a rival to Sceptic can always play so as to obtain current evidence as good as Sceptic’s reduced maximum. We characterize the functions that can achieve such reductions. Because these functions may impose only modest reductions, we think of our result as a method of insuring against loss of evidence. In the context of an actual market, it is a method of insuring against the loss of what an investor has gained so far.

Article
Panov V. Statistics and Probability Letters. 2017. Vol. 129. P. 379-386.

In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions of the sums due to various relations between these parameters.

Article
Durio A., Y.Y.Nikitin. Statistics and Probability Letters. 2016. Vol. 117. No. 10. P. 136-143.

The efficiency of distribution-free integrated goodness-of-fit tests was studied by Henze and Nikitin (2000, 2002) under location alternatives. We calculate local Bahadur efficiencies of these tests under more realistic generalized skew alternatives. They turn out to be unexpectedly high.

Article
Gushchin A. A., Küchler U. Statistics and Probability Letters. 2004. Vol. 70. No. 1. P. 19-24.

The authors consider the Ito stochastic differential equation

dX(t)=(aX(t)+f(X(t-r)))dt+σX(t)dW(t),t≥0

with scalar Brownian motion W and a locally bounded measurable function f. Expressing the solution X in terms of the classical geometric Brownian motion, it can be proved that for a positive initial segment (X(s),-r≤s≤0) and non-negative f, the process X remains positive a.s. On the other hand, the authors establish a condition on a, σ and f such that the solution process with positive initial condition attains zero in finite time a.s. This condition is for instance satisfied if f is non-increasing with at least linear growth while a and σ are arbitrary.

Article
Panov V. Statistics and Probability Letters. 2019. Vol. 146. P. 80-84.

In this paper, we consider some properties of the model constructed from the one-dimensional stable processes by changing the time to a non-decreasing Lévy process. Our first result reveals a relation between this class of processes and the class of time-changed Brownian motions. Moreover, we describe the CGMY (Carr-Geman-Madan-Yor) model as subordinated stable process, and show the representation of the Lévy density of the corresponding subordinator via the Mellin–Barnes integral.