arXiv subjects

Sergey V. Malov

Publications and source records attributed to Sergey V. Malov.

2 recordsLinked to original sources

arXiv2026

Practical properties of the CUSUM process

We establish new properties of the Lindley process, also known as the waiting time process or the cumulative-sum (CUSUM) process, as well as its running maximum. Unlike many other authors, the study focuses on exact and asymptotic expressions for the moment generating function (MGF) of CUSUM. It includes precise finite-sample expressions for the MGF and moments of the process, along with fast recursive computing algorithms, lower and upper bounds, and the classification of large-sample asymptotics of the CUSUM MGF. Results are applied to single, multiple, and transient change-point problems, for the calculation of thresholds that provide a desired control of familywise false alarm rates, as well as the quantiles of queuing processes and probabilities of their large deviation at least once over a given finite time interval.

math.PR↗

arXiv2019

Uniform convergence rate of nonparametric maximum likelihood estimator for the current status data with competing risks

We study the uniform convergence rate of the nonparametric maximum likelihood estimator (MLE) for the sub-distribution functions in the current status data with competing risks model. It is known that the MLE have $L^2$-norm convergence rate $O_P(n^{-1/3})$ in the absolutely continuous case, but there is no arguments for the same rate of uniform convergence. We specify conditions for the uniform convergence rate $O_P(n^{-1/3}\log^{1/3} n)$ of the MLE for the sub-distribution functions of competing risks on finite intervals. The obtained result refines known uniform convergence rate in the particular case of current status data. The main result is applied in order to get the uniform convergence rate of the MLE for the survival function of failure time in the current status right-censored data model.

math.ST↗