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We propose a two-phase systematical framework for approximation algorithm design and analysis via Lyapunov function. The first phase consists of using Lyapunov function as an input and outputs a continuous-time approximation algorithm with…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
Parametric analysis is a powerful tool for designing modern embedded systems, because it permits to explore the space of design parameters, and to check the robustness of the system with respect to variations of some uncontrollable…
We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambda-calculus can simulate each other within a polynomial…
In this paper, we investigate the asymptotic properties of Le Cam's one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily…
With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local…
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
This paper deals with the dimension reduction for high-dimensional time series based on common factors. In particular we allow the dimension of time series $p$ to be as large as, or even larger than, the sample size $n$. The estimation for…
When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in each iteration. In this…
This paper considers both the least squares and quasi-maximum likelihood estimation for the recently proposed scalable ARMA model, a parametric infinite-order vector AR model, and their asymptotic normality is also established. It makes…
Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…
Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of…
In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning…
Model-free adaptive optimization methods are capable of optimizing unknown, time-varying processes even when other optimization methods are not. However, their practical application is often limited by perturbations that are used to gather…
When Perturbation Analysis (PA) yields unbiased sensitivity estimators for expected-value performance functions in discrete event dynamic systems, it can be used for performance optimization of those functions. However, when PA is known to…
Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees,…
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite…
This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…