Related papers: Statistical inference for discrete-time samples fr…
We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound.…
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…
Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function,…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…
We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
This paper is about the state estimation of timed probabilistic discrete event systems. The main contribution is to propose general procedures for developing state estimation approaches based on artificial neural networks. It is assumed…
This note considers the problem of statistical inference of the parameters of the input process to a queue from periodic workload observations. The main focus is the open problem of constructing statistically efficient estimators for a…
Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…