Related papers: Smooth Distribution Function Estimation for Lifeti…
This paper proposes an original approach to better understanding the behavior of robust scatter matrix $M$-estimators. Scatter matrices are of particular interest for many signal processing applications since the resulting performance…
Recently there have been increasing interests in learning and inference with implicit distributions (i.e., distributions without tractable densities). To this end, we develop a gradient estimator for implicit distributions based on Stein's…
Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting…
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…
By the continuous mapping theorem, if a sequence of $d$-dimensional random vectors $(\mathbf{W}_n)_{n\geq1}$ converges in distribution to a multivariate normal random variable $\Sigma^{1/2}\mathbf{Z}$, then the sequence of random variables…
We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.
We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
In many radar scenarios, the radar target or the medium is assumed to possess randomly varying parts. The properties of a target are described by a random process known as the spreading function. Its second order statistics under the WSSUS…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
We introduce a new method to prove lower estimates for the approximation error of general linear operators with smooth range in terms of classical moduli of smoothness and related $K$-functionals. In addition, we explicitly show how to…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
We propose a novel method for forecasting the temporal evolution of probability distributions observed at discrete time points. Extending the Dynamic Probability Density Decomposition (DPDD), we embed distributional dynamics into…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
We study the problem of estimating the score function of an unknown probability distribution $\rho^*$ from $n$ independent and identically distributed observations in $d$ dimensions. Assuming that $\rho^*$ is subgaussian and has a…
This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…
The sum of proper divisors function $s(n)$ has been studied for more than 2000 years. In this paper we study statistical properties of the related function $S_s(n) := \sum_{d \mid n} s(d)$. This function arises from a generalization of the…
We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…