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It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown…
Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a…
This study addresses the often-overlooked issue of measurability at intermediate points when applying Taylor's theorems to random functions and random vectors (e.g., likelihood functions with respect to estimators) in statistics. Classical…
We consider the problem of estimating the mean $f$ of a Gaussian vector $Y$ with independent components of common unknown variance $\sigma^{2}$. Our estimation procedure is based on estimator selection. More precisely, we start with an…
We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of observations. Motivated by this problem, in this contribution we first investigate the extremes of Gaussian fields…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable.…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
Fermi's golden rule is of great importance in quantum dynamics. However, in many textbooks on quantum mechanics, its contents and limitations are obscured by the approximations and arguments in the derivation, which are inevitable because…
Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
Treating the fermionic ground state problem as a constrained stochastic optimization problem, a formalism for fermionic quantum Monte Carlo is developed that makes no reference to a trial wavefunction. Exchange symmetry is enforced by…
The Frank-Wolfe method has become increasingly useful in statistical and machine learning applications, due to the structure-inducing properties of the iterates, and especially in settings where linear minimization over the feasible set is…
In this paper we introduce randomized $t$-type statistics that will be referred to as randomized pivots. We show that these randomized pivots yield central limit theorems with a significantly smaller magnitude of error as compared to that…
Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…