Related papers: Robust and Efficient Parameter Estimation for Disc…
In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…
The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems are established by taking a nonparametric approach in the context of a…
Markov decision processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for \emph{ambiguity sets} which give a set of possible distributions over parameter sets.…
We consider the problem of variable screening in ultra-high dimensional generalized linear models (GLMs) of non-polynomial orders. Since the popular SIS approach is extremely unstable in the presence of contamination and noise, we discuss a…
This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…
Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential…
The increasing integration of distributed energy resources (DERs) is transforming power systems into complex, decentralized networks, particularly at the distribution level, where active distribution networks (ADNs) introduce new challenges…
Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…
In this paper, we propose a robust data-driven process model whose hyperparameters are robustly estimated using the Schweppe-type generalized maximum likelihood estimator. The proposed model is trained on recorded time-series data of…
The issue of discrete probability estimation for samples of small size is addressed in this study. The maximum likelihood method often suffers over-fitting when insufficient data is available. Although the Bayesian approach can avoid…
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved…
We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…
By integrating two powerful methods of density reduction and intrinsic dimensionality estimation, a new data-driven method, referred to as OLPP-MLE (orthogonal locality preserving projection-maximum likelihood estimation), is introduced for…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to classical techniques based on maximum likelihood and related methods. Basu et al. (1998) introduced the density power divergence…
We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov…
Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable…
The inherent complexity of biological agents often leads to motility behavior that appears to have random components. Robust stochastic inference methods are therefore required to understand and predict the motion patterns from time…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…