Related papers: Statistical inference for discrete-time samples fr…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time,…
We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…
Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…