Related papers: Deconvolution with unknown error distribution

Many statistical models seek relationship between variables via subspaces of reduced dimensions. For instance, in factor models, variables are roughly distributed around a low dimensional subspace determined by the loading matrix; in mixed…

We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…

This paper focuses on estimating the invariant density function $f_X$ of the strongly mixing stationary process $X_t$ in the multiplicative measurement errors model $Y_t = X_t U_t$, where $U_t$ is also a strongly mixing stationary process.…

We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…

It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation procedure can be vulnerable to corrupted data points, which often pushes the…

Over the last few years, debiased estimators have been proposed in order to establish rigorous confidence intervals for high-dimensional problems in machine learning and data science. The core argument is that the error of these estimators…

We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with $\sqrt{n}$-rate on the assumption that the smoothness of the functionals is larger than the…

Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…

We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…

We consider X 1 ,. .. , X n a sample of data on the circle S 1 , whose distribution is a twocomponent mixture. Denoting R and Q two rotations on S 1 , the density of the X i 's is assumed to be g(x) = pf (R --1 x) + (1 -- p)f (Q --1 x),…

Uncertainty estimation is an essential step in the evaluation of the robustness for deep learning models in computer vision, especially when applied in risk-sensitive areas. However, most state-of-the-art deep learning models either fail to…

In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous…

We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…

We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…

This work resolves the following question in non-Euclidean statistics: Is it possible to consistently estimate the Fr\'echet mean set of an unknown population distribution, with respect to the Hausdorff metric, when given access to…

Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…

We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…

Let $(X_i)_{i\geq 1}$ be an i.i.d. sample on $\RRR^d$ having density $f$. Given a real function $\phi$ on $\RRR^d$ with finite variation and given an integer valued sequence $(j_n)$, let $\fn$ denote the estimator of $f$ by wavelet…