Related papers: $V$-statistics and Variance Estimation

Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma Z_i$ and $Y_i$ and $Z_i$ are independent. Assume that unobservable $Y$'s are distributed as a random variable $UV,$ where $U$ and $V$ are independent, $U$ has a Bernoulli…

Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…

This work develops formal statistical inference procedures for machine learning ensemble methods. Ensemble methods based on bootstrapping, such as bagging and random forests, have improved the predictive accuracy of individual trees, but…

We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of…

The increasing use of vine copulas in high-dimensional settings, where the number of parameters is often of the same order as the sample size, calls for asymptotic theory beyond the traditional fixed-$p$, large-$n$ framework. We establish…

Let $\{X_n, n \ge 1\}$ be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on $\{X_n, n \ge 1\}$ holds. We look at U-statistics based on…

We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…

In another related work, U-statistics were used for non-asymptotic "average-case" analysis of random compressed sensing matrices. In this companion paper the same analytical tool is adopted differently - here we perform non-asymptotic…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

This paper develops a variance estimation framework for matching estimators that enables valid population inference for treatment effects. We provide theoretical analysis of a variance estimator that addresses key limitations in the…

Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…

A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$,…

An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…

We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…

We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…