Related papers: Design based incomplete U-statistics

We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…

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…

A weighted U-statistic based on a random sample X_1,...,X_n has the form U_n=\sum_{1\le i,j\le n}w_{i-j}K(X_i,X_j), where K is a fixed symmetric measurable function and the w_i are symmetric weights. A large class of statistics can be…

We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984)…

This paper considers distributed statistical inference for general symmetric statistics %that encompasses the U-statistics and the M-estimators in the context of massive data where the data can be stored at multiple platforms in different…

In this paper, we study the asymptotic distribution of some U-statistics whose entries are functions of empirical moments computed from non-overlapping consecutive blocks of an underlying weakly dependent process. The length of these blocks…

We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…

Non-parametric two-sample tests based on energy distance or maximum mean discrepancy are widely used statistical tests for comparing multivariate data from two populations. While these tests enjoy desirable statistical properties, their…

Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…

Bagging is a useful method for large-scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for $M$-estimation problems but with massive datasets.…

For many machine learning problems, data is abundant and it may be prohibitive to make multiple passes through the full training set. In this context, we investigate strategies for dynamically increasing the effective sample size, when…

Inference in clustering is paramount to uncovering inherent group structure in data. Clustering methods which assess statistical significance have recently drawn attention owing to their importance for the identification of patterns in high…

We derive a new representation for $U$- and $V$-statistics. Using this representation, the asymptotic distribution of $U$- and $V$-statistics can be derived by a direct application of the Continuous Mapping theorem. That novel approach not…

This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…

In this paper, we aim to develop stochastic hard thresholding algorithms for the important problem of AUC maximization in imbalanced classification. The main challenge is the pairwise loss involved in AUC maximization. We overcome this…

Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…

In this paper, a novel test for testing whether data are Missing Completely at Random is proposed. Asymptotic properties of the test are derived utilizing the theory of non-degenerate U-statistics. It is shown that the novel test statistic…

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…

Partial observability is a common challenge in many reinforcement learning applications, which requires an agent to maintain memory, infer latent states, and integrate this past information into exploration. This challenge leads to a number…