Related papers: Estimation of distributions, moments and quantiles…
We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
This paper focuses on the problem of the estimation of the cumulative hazard function of a distribution on a general complete separable metric space when the data points are subject to censoring by an arbitrary adapted random set. A problem…
We consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to…
Data observed at high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or a smooth random function, and measurement error. Supposing…
In supervised learning, the estimation of prediction error on unlabeled test data is an important task. Existing methods are usually built on the assumption that the training and test data are sampled from the same distribution, which is…
Motivated by questions in lossy data compression and by theoretical considerations, we examine the problem of estimating the rate-distortion function of an unknown (not necessarily discrete-valued) source from empirical data. Our focus is…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
We study a nonlinear regression problem of fitting a circle (or a circular arc) to scattered data. We prove that under any standard assumptions on the statistical distribution of errors that are commonly adopted in the literature, the…
To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the "missing at random" and "no unmeasured confounder" assumptions. However, these assumptions are unverifiable…
We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and…
We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
Given samples (x_1,...,x_m) and (z_1,...,z_n) which we believe are independent realizations of random variables X and Z respectively, where we further believe that Z=X+Y with Y independent of X, the problem is to estimate the distribution…
In this paper we consider the kernel estimators of a distribution function defined by the stochastic approximation algorithm when the observation are contamined by measurement errors. It is well known that this estimators depends heavily on…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test…