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Machine learning-based performance models are increasingly being used to build critical job scheduling and application optimization decisions. Traditionally, these models assume that data distribution does not change as more samples are…
We consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extension. In both cases, we show that it is continuous with…
We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…
Long memory in the sense of slowly decaying autocorrelations is a stylized fact in many time series from economics and finance. The fractionally integrated process is the workhorse model for the analysis of these time series. Nevertheless,…
We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields…
We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the…
We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity -- what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
Machine learning models based on temporal point processes are the state of the art in a wide variety of applications involving discrete events in continuous time. However, these models lack the ability to answer counterfactual questions,…
Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…
In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
Employing recent results of Robinson (2005) we consider the asymptotic properties of conditional-sum-of-squares (CSS) estimates of parametric models for stationary time series with long memory. CSS estimation has been considered as a rival…