Related papers: Minimax Optimal Additive Functional Estimation wit…
Consider the problem of estimating the Shannon entropy of a distribution over $k$ elements from $n$ independent samples. We show that the minimax mean-square error is within universal multiplicative constant factors of $$\Big(\frac{k }{n…
We consider estimation of a step function $f$ from noisy observations of a deconvolution $\phi*f$, where $\phi$ is some bounded $L_1$-function. We use a penalized least squares estimator to reconstruct the signal $f$ from the observations,…
Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a…
The problem of optimal estimation of functionals $A\xi =\sum\nolimits_{k=0}^{\infty }{}a(k)\xi (k)$ and ${{A}_{N}}\xi =\sum\nolimits_{k=0}^{N}{}a(k)\xi (k)$ which depend on the unknown values of stochastic sequence $\xi (k)$ with stationary…
We study the problem of aggregation of estimators when the estimators are not independent of the data used for aggregation and no sample splitting is allowed. If the estimators are deterministic vectors, it is well known that the minimax…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
Given $n$ i.i.d. observations, we study the problem of estimating the spectrum of weighted Laplace operators of the form $\Delta_f=\Delta + \alpha \nabla \log f\cdot \nabla$, where $f$ is a positive probability density on a known compact…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
This paper studies an asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\phi$ is a known directionally differentiable function and $\theta_0$ is estimated by $\hat \theta_n$. In these settings,…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…
Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
We analyze the problem of discrete distribution estimation under $\ell_1$ loss. We provide non-asymptotic upper and lower bounds on the maximum risk of the empirical distribution (the maximum likelihood estimator), and the minimax risk in…
Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use $O( \log (\beta \Delta) \log (\epsilon^{-1}))$…