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We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum…
Bogdan et al. established a new criterion to determine the existence of a maximum likelihood estimator in discrete exponential families. It uses the notion of the set of uniqueness, which allows to apply the problem to the Ising model from…
When a finite order vector autoregressive model is fitted to VAR($\infty$) data the asymptotic distribution of statistics obtained via smooth functions of least-squares estimates requires care. L\"utkepohl and Poskitt (1991) provide a…
In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows. Under the widely adopted capacity-source condition framework…
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn,…
We introduce the Meta Highly-Adaptive-Lasso Minimum Loss Estimator (M-HAL-MLE), a novel ensemble approach for estimating functional parameters of realistically modeled data distribution from independent and identically distributed…
In this paper we propose and study a version of the Dyadic Classification and Regression Trees (DCART) estimator from Donoho (1997) for (fixed design) quantile regression in general dimensions. We refer to this proposed estimator as the…
Adaptively collected data has become ubiquitous within modern practice. However, even seemingly benign adaptive sampling schemes can introduce severe biases, rendering traditional statistical inference tools inapplicable. This can be…
A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…
Let $f$ be a nonincreasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between $f$ and its Grenander-type estimator on sub-intervals of…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these…
Estimating a large alphabet probability distribution from a limited number of samples is a fundamental problem in machine learning and statistics. A variety of estimation schemes have been proposed over the years, mostly inspired by the…
In this study, we propose a new method for constructing UCB-type algorithms for stochastic multi-armed bandits based on general convex optimization methods with an inexact oracle. We derive the regret bounds corresponding to the convergence…
Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift,…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…
If $\mu$ is a distribution over the $d$-dimensional Boolean cube $\{0,1\}^d$, our goal is to estimate its mean $p\in[0,1]^d$ based on $n$ iid draws from $\mu$. Specifically, we consider the empirical mean estimator $\hat p_n$ and study the…
Loss tomography has received considerable attention in recent years and a number of estimators have been proposed. Although most of the estimators claim to be the maximum likelihood estimators, the claim is only partially true since the…
Following Baraud, Birg\'e and Sart (2017), we pursue our attempt to design a robust universal estimator of the joint ditribution of $n$ independent (but not necessarily i.i.d.) observations for an Hellinger-type loss. Given such…
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally…