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The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…
Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…
This paper deals with the problem of finding suboptimal values of an unknown function on the basis of measured data corrupted by bounded noise. As a prior, we assume that the unknown function is parameterized in terms of a number of basis…
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
In this paper we consider the problem of linear unmixing hidden random variables defined over the simplex with additive Gaussian noise, also known as probabilistic simplex component analysis (PRISM). Previous solutions to tackle this…
This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized…
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the…
We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…
When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…
This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
This work studies the computational aspects of multivariate convex regression in dimensions $d \ge 5$. Our results include the \emph{first} estimators that are minimax optimal (up to logarithmic factors) with polynomial runtime in the…
Let $Y\in\R^n$ be a random vector with mean $s$ and covariance matrix $\sigma^2P_n\tra{P_n}$ where $P_n$ is some known $n\times n$-matrix. We construct a statistical procedure to estimate $s$ as well as under moment condition on $Y$ or…
Based on the convex least-squares estimator, we propose two different procedures for testing convexity of a probability mass function supported on N with an unknown finite support. The procedures are shown to be asymptotically calibrated.
We study the problem of parameter estimation for discretely observed stochastic differential equations driven by small fractional noise. Under some conditions, we obtain strong consistency and rate of convergence of the least square…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…