Searcharxiv⌕ Search

arXiv subjects

Andrei Novikov

Publications and source records attributed to Andrei Novikov.

3 recordsLinked to original sources
arXiv2021

A computational approach to the Kiefer-Weiss problem for sampling from a Bernoulli population

We present a computational approach to solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the proposed algorithms are implemented in the form of R program code. Using the developed computer program, we numerically compare the optimal tests with the respective sequential probability ratio test (SPRT) and the fixed sample size test, for a wide range of hypothesized values and type I and type II errors. The results are compared with those of D.~Freeman and L.~Weiss (Journal of the American Statistical Association, 59(1964)). The R source code for the algorithms of construction of optimal sampling plans and evaluation of their characteristics is available at https://github.com/tosinabase/Kiefer-Weiss.

stat.ME↗
arXiv2021

Mixed limits of some functional spaces

In this article we propose a conception of mixed limits of functional spaces as the case, when the upper limit (projective limit of inductive limits) and the lower limit (inductive limit of projective limits) coincide as topological spaces, which are generalization of inductive and projective limits of functional spaces. We show a cases where these mixed limits are naturally obtained as the limit spaces of non-commutative $L_p$-type spaces associated with the sequence of operators. Also, we obtain results on the properties of limit spaces, we show that limit spaces of Banach algebras are (LF)-spaces, if they converge.

math.OA↗