Related papers: On universal estimates for binary renewal processe…
We study universal consistency of non-i.i.d. processes in the context of online learning. A stochastic process is said to admit universal consistency if there exists a learner that achieves vanishing average loss for any measurable response…
We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point…
We present a solution to the problem of understanding a system that produces a sequence of temporally ordered observations. Our solution is based on generating and interpreting a set of temporal decision rules. A temporal decision rule is a…
We consider a problem of replication of random vectors by ordinary integrals in the setting when a underlying random variable is generated by a Wiener process. The goal is to find an optimal adapted process such that its cumulative integral…
We consider renewal processes where events, which can for instance be the zero crossings of a stochastic process, occur at random epochs of time. The intervals of time between events, $\tau_{1},\tau_{2},...$, are independent and identically…
Certain renewal theorems are extended to the case that the rate of the renewal process goes to 0 and, more generally, to the case that the drift of the random walk goes to infinity. These extensions are motivated by and applied to the…
When faced with sequential decision-making problems, it is often useful to be able to predict what would happen if decisions were made using a new policy. Those predictions must often be based on data collected under some previously used…
We consider two models of two-units repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using…
We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of…
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…
We construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally we compute the rate of convergence in a particular case.
Recurrence rate, determinism, average line length, and entropy of line lengths are measures of complexity in recurrence quantification analysis, that help to understand the structure, predictability and complexity of dynamical systems. In…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…
Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound).…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
Large deviations for the local time of a process $X_t$ are investigated, where $X_t=x_i$ for $t \in [S_{i-1},S_i[$ and $(x_j)$ are i.i.d.\ random variables on a Polish space, $S_j$ is the $j$-th arrival time of a renewal process depending…
In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is…