Related papers: Consistance d'un estimateur de minimum de variance…
We study the problem of estimating the mean of a random vector in $\mathbb{R}^d$ based on an i.i.d.\ sample, when the accuracy of the estimator is measured by a general norm on $\mathbb{R}^d$. We construct an estimator (that depends on the…
This paper proposes minimum distance inference for a structural parameter of interest, which is robust to the lack of identification of other structural nuisance parameters. Some choices of the weighting matrix lead to asymptotic…
The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…
We study the k nearest neighbors problem in the plane for general, convex, pairwise disjoint sites of constant description complexity such as line segments, disks, and quadrilaterals and with respect to a general family of distance…
We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some…
The statistical properties of estimator using covariance matrix for the account of point-to-point correlations due to systematic errors are analyzed. It is shown that the covariance matrix estimator (CME) is consistent for the realistic…
The field of machine have seen rising applications of equivariance criterion. However, there is no systematic way to justify its usage, including why it works, whether there is an optimal solution and if so, what form it carries. In this…
We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these…
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…
I analyze a linear instrumental variables model with a single endogenous regressor and many instruments. I use invariance arguments to construct a new minimum distance objective function. With respect to a particular weight matrix, the…
We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use…
Roughly speaking, Ekeland's Variational Principle (EkVP) (J. Math. Anal. Appl. 47 (1974), 324--353) asserts the existence of strict minima of some perturbed versions of lower semicontinuous functions defined on a complete metric space.…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Sequential minimum optimization is a machine-learning global search training algorithm. It is applicable when the functional dependence of the cost function on a tunable parameter given the other parameters can be cheaply determined. This…
Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples.…
Regression branch of Machine Learning purely focuses on prediction of continuous values. The supervised learning branch has many regression based methods with parametric and non-parametric learning models. In this paper we aim to target a…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
Studies on various facets of pattern classification is often imperative while working with multi-dimensional samples pertaining to diverse application scenarios. In this notion, weighted dimension-based distance measure has been one of the…
Given an $n$-sample of random vectors $(X_i,Y_i)_{1 \leq i \leq n}$ whose joint law is unknown, the long-standing problem of supervised classification aims to \textit{optimally} predict the label $Y$ of a given a new observation $X$. In…