A. N. Kolmogorov contributed much to mathematical statistics, both through his own statistical works and through the researches of his students and disciples in statistics. But the case will be made that he influenced statistics still more through his general mathematical concepts and approaches. This paper gives some examples of unexpected applications of Kolmogorov's ideas in topics of nonparametric statistics.
"The Unfathomable Influence of Kolmogorov." Ann. Statist. 18 (3) 987 - 998, September, 1990. https://doi.org/10.1214/aos/1176347735