Related papers: Predictive density estimators with integrated $L_1…
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…
Let $p_n(y)=\sum_k\hat{\alpha}_k\phi(y-k)+\sum_{l=0}^{j_n-1}\sum_k\hat {\beta}_{lk}2^{l/2}\psi(2^ly-k)$ be the linear wavelet density estimator, where $\phi$, $\psi$ are a father and a mother wavelet (with compact support),…
We study the problem of nonparametric estimation of density functions with a product form on the domain $\triangle=\{( x_1, \ldots, x_d)\in \mathbb{R}^d, 0\leq x_1\leq \dots \leq x_d \leq 1\}$. Such densities appear in the random truncation…
We study the problem of model selection type aggregation with respect to the Kullback-Leibler divergence for various probabilistic models. Rather than considering a convex combination of the initial estimators $f_1, \ldots, f_N$, our…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…
For normal canonical models with $X \sim N_p(\theta, \sigma^{2} I_{p}), \;\; S^{2} \sim \sigma^{2}\chi^{2}_{k}, \;{independent}$, we consider the problem of estimating $\theta$ under scale invariant squared error loss $\frac{\|d-\theta…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
As it is known, universal codes, which estimate the entropy rate consistently, exist for stationary ergodic sources over finite alphabets but not over countably infinite ones. We generalize universal coding as the problem of universal…
There has been growing interest in the AI community for precise uncertainty quantification. Conditional density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in…
For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
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…
Popular debiased estimation methods for causal inference -- such as augmented inverse propensity weighting and targeted maximum likelihood estimation -- enjoy desirable asymptotic properties like statistical efficiency and double robustness…
Causal inference problems often involve continuous treatments, such as dose, duration, or frequency. However, identifying and estimating standard dose-response estimands requires that everyone has some chance of receiving any level of the…
We consider the setting of linear regression in high dimension. We focus on the problem of constructing adaptive and honest confidence sets for the sparse parameter \theta, i.e. we want to construct a confidence set for theta that contains…