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Inspired by logistic regression, we introduce a regression model for data tuples consisting of a binary response and a set of covariates residing in a metric space without vector structures. Based on the proposed model we also develop a…
For multivariate data, Tukey's half-space depth is one of the most popular depth functions available in the literature. It is conceptually simple and satisfies several desirable properties of depth functions. The Tukey median, the…
We consider a joint asymptotic framework for studying semi-nonparametric regression models where (finite-dimensional) Euclidean parameters and (infinite-dimensional) functional parameters are both of interest. The class of models in…
A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference. Yet, the existing developments such as Winsorization,…
We describe a new recentered confidence sphere for the mean, theta, of a multivariate normal distribution. This sphere is centred on the positive-part James-Stein estimator, with radius that is a piecewise cubic Hermite interpolating…
Conformal prediction is a model-free machine learning method for constructing prediction regions at a guaranteed coverage probability level. However, a data scientist often faces three challenges in practice: (i) the determination of a…
We study the harmonic mean of non-zero complex-valued random variables (complex harmonic mean) and establish several geometric estimates and bounds. In contrast to the classical positive-valued case, complex harmonic means may lie outside…
We introduce a class of regularized M-estimators of multivariate scatter and show, analogous to the popular spatial sign covariance matrix (SSCM), that they possess high breakdown points. We also show that the SSCM can be viewed as an…
The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…
We develop large sample theory including nonparametric confidence regions for $r$-dimensional ridges of probability density functions on $\mathbb{R}^d$, where $1\leq r<d$. We view ridges as the intersections of level sets of some special…
We give the first differentially private algorithms that estimate a variety of geometric features of points in the Euclidean space, such as diameter, width, volume of convex hull, min-bounding box, min-enclosing ball etc. Our work relies…
Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g.,…
Identification of multinomial choice models is often established by using special covariates that have full support. This paper shows how these identification results can be extended to a large class of multinomial choice models when all…
This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…
Conformal prediction provides a distribution-free framework for uncertainty quantification. This study explores the application of conformal prediction in scenarios where covariates are missing, which introduces significant challenges for…
The goal of this paper is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of the…
This paper investigates the asymptotic properties of parameter estimation for the Ewens--Pitman partition with parameters $0<\alpha<1$ and $\theta>-\alpha$. Especially, we show that the maximum likelihood estimator (MLE) of $\alpha$ is…
Multivariate linear regression is a fundamental statistical task, but classical estimators such as ordinary least squares are highly sensitive to outliers. These may occur as casewise outliers that affect entire observations, or as outlying…
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…
Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing…