Related papers: Estimation of a convex discrete distribution
We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
We constraint on computer the best linear unbiased generalized statistics of random field for the best linear unbiased generalized statistics of an unknown constant mean of random field and derive the numerical generalized least-squares…
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…
The discrete moment problem is a foundational problem in distribution-free robust optimization, where the goal is to find a worst-case distribution that satisfies a given set of moments. This paper studies the discrete moment problems with…
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…
We study the problem of estimating multiple discrete unimodal distributions, motivated by search behavior analysis on a real-world platform. To incorporate prior knowledge of precedence relations among distributions, we impose stochastic…
We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…
Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support $S$. Under the mild assumption that $S$ is $r$-convex, the smallest $r$-convex set which contains the…
In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…
We find the local rate of convergence of the least squares estimator (LSE) of a one dimensional convex regression function when (a) a certain number of derivatives vanish at the point of interest, and (b) the true regression function is…
Estimation of linear functionals from observed data is an important task in many subjects. Juditsky & Nemirovski [The Annals of Statistics 37.5A (2009): 2278-2300] propose a framework for non-parametric estimation of linear functionals in a…
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
We study distributed estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in $\R^d$. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension…
We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…
The problem we concentrate on is as follows: given (1) a convex compact set $X$ in ${\mathbb{R}}^n$, an affine mapping $x\mapsto A(x)$, a parametric family $\{p_{\mu}(\cdot)\}$ of probability densities and (2) $N$ i.i.d. observations of the…