Linear prediction of sums of sequential minima

Valery Borisovich Nevzorov, Valeriia Savinova and Alexei Stepanov

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 16, 5446-5454

Abstract: Let X1,…,Xn be independent and identically distributed continuous nonnegative random variables and mn=min{X1,…,Xn} be the sample minimum. In the present paper, we find the best linear predictors E(m1+…+mn|mj=x) and E(m1+…+mn|m1=x1,…,mj=xj) and then analyze their behavior by using simulation in the cases of the standard exponential and uniform distributions.

Date: 2022
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DOI: 10.1080/03610926.2020.1841237

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