3 papers
math.PR2024
Ordinary and logarithmical convexity of moment generating function
M. R. Formica, E. Ostrovsky, L. Sirota
We establish an ordinary as well as a logarithmical convexity of the Moment Generating Function (MGF) for the centered random variable and vector (r.v.) satisfying the Kramer's con…
math.PR2024
Exact exponential tail estimation for sums of independent centered random variables, under natural norming, with applications to the theory of U-statistics
M. R. Formica, E. Ostrovsky, L. Sirota
We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of…
math.ST2024
Adaptive smoothness of function estimation in the three classical problems of the non-parametrical statistic in the three classical problems of the non-parametrical statistic
M. R. Formica, E. Ostrovsky, L. Sirota
We offer in this short report the so-called adaptive functional smoothness estimation in the Hilbert space norm sense in the three classical problems of non-parametrical statistic:…