Related papers: Design based incomplete U-statistics
This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n \to \infty$ with fixed kernel size $k$. Under some regularity conditions,…
This paper studies the Gaussian and bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when the dimension $d$ is large. A two-step Gaussian approximation…
We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…
Neural networks have achieved dramatic improvements in recent years and depict the state-of-the-art methods for many real-world tasks nowadays. One drawback is, however, that many of these models are overparameterized, which makes them both…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However,…
Given data drawn from an unknown distribution, $D$, to what extent is it possible to ``amplify'' this dataset and output an even larger set of samples that appear to have been drawn from $D$? We formalize this question as follows: an…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
Motivated by some common-change point tests, we investigate the asymptotic distribution of the U-statistic process $U_n(t)=\sum_{i=1}^{[nt]}\sum_{j=[nt]+1}^n h(X_i,X_j)$, $0\leq t\leq 1$, when the underlying data are long-range dependent.…
Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…
Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…
Imbalanced classification often causes standard training procedures to prioritize the majority class and perform poorly on rare but important cases. A classic and widely used remedy is to augment the minority class with synthetic samples,…
This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…
Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…
Imbalanced data are frequently encountered in real-world classification tasks. Previous works on imbalanced learning mostly focused on learning with a minority class of few samples. However, the notion of imbalance also applies to cases…
Adaptive designs have been proposed for clinical trials in which the nuisance parameters or alternative of interest are unknown or likely to be misspecified before the trial. Whereas most previous works on adaptive designs and mid-course…
An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations…
Asymptotic efficiency theory is one of the pillars in the foundations of modern mathematical statistics. Not only does it serve as a rigorous theoretical benchmark for evaluating statistical methods, but it also sheds light on how to…
In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…