Related papers: Stein Estimation for Infinitely Divisible Laws
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network…
The balance equations of energy-momentum and spin together with Einstein's field equations are investigated by the Liu procedure to find constraints for the constitutive equations in such a way that the Second Law is satisfied. Special…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…
We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit…
This paper focuses on the Bregman divergence defined by the reciprocal function, called the inverse divergence. For the loss function defined by the monotonically increasing function $f$ and inverse divergence, the conditions for the…
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…
We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various…
We extend Stein's method to include dependence with respect to an auxiliary random variable, for conditional laws for which Stein's characterizations do exist.
We solve the generalised quantum Stein's lemma, proving that the Stein exponent associated with entanglement testing, namely, the quantum hypothesis testing task of distinguishing between $n$ copies of an entangled state $\rho_{AB}$ and a…
Optimal stopping is the problem of deciding when to stop a stochastic system to obtain the greatest reward, arising in numerous application areas such as finance, healthcare and marketing. State-of-the-art methods for high-dimensional…
This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population…
In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [1] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In…
We establish the necessary and sufficient conditions for unbiased estimation in multi-parameter estimation tasks. More specifically, we first consider quantum state estimation, where multiple parameters are encoded in a quantum state, and…
Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…
We derive formulas for the moments of the ruin time in a L\'evy risk model and use these to determine the asymptotic behavior of the moments of the ruin time as the initial capital tends to infinity. In the special case of the perturbed…
We consider a risk-sensitive continuous-time Markov decision process over a finite time duration. Under the conditions that can be satisfied by unbounded transition and cost rates, we show the existence of an optimal policy, and the…
We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…
By a delicate analysis for the Stein's equation associated to the $\alpha$-stable law approximation with $\alpha \in (0,2)$, we prove a quantitative stable central limit theorem in Wasserstein type distance, which generalizes the results in…