arXiv subjects

Malo Sahin

Publications and source records attributed to Malo Sahin.

3 recordsLinked to original sources

arXiv2026

Multi-state model with temporal-consistent survival analysis for homogeneous Markov chains

In this study, we consider sequences drawn from time-homogeneous Markov chains and introduce a novel approach for estimating first hitting-time distributions to specified terminal states. Our method- ology is based on the temporal-consistent survival analysis that facilitates the construction of consistent estimators of the distributions from any estimates of the transition rate and transition probabilities. In this line of work, we also discuss the issue of cured individuals with chains that never reach a termi- nal state, and propose an estimator of the cure rate. Furthermore, we derive non-asymptotic theoretical guarantees for our approach and apply our methodology with kernel type estimators. The latter approach is illustrated in a simulation study using generic data and a real-life application involving patients un- dergoing bone marrow transplants.

math.ST↗

arXiv2025

Ratio limit theorem for renewal processes

We consider a renewal process which models a cumulative shock model that fails when the accumulation of shocks up-crosses a certain threshold. The ratio limit properties of the probabilities of non-failure after n cumulative shocks are studied. We establish that the ratio of survival probabilities converges to the probability that the renewal epoch equals zero. This limit holds for any renewal process, subject only to mild regularity conditions on the individual shock random variable. Precisions on the rates of convergence are provided depending on the support structure and the regularity of the distribution. Arguments are provided to highlight the coherence between this new results and the pre-existing results on the behavior of summands of i.i.d. real random variables.

math.PR↗

arXiv2025

A dependent and censored first hitting-time model with compound Poisson processes

We consider a bivariate first hitting-time model in which durations are the crossing times of dependent compound Poisson processes with fixed thresholds. The identifiability of the model is discussed, and likelihood estimators of the model parameters are proposed. We obtain the asymptotic properties of the estimators and underline their finite sample performance with a simulation study on synthetic data. The practical applicability of our approach is demonstrated by an application using data from patients suffering from mushroom poisoning.

stat.ME↗