Related papers: Simultaneous Inference for High Dimensional Mean V…
Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…
We present a randomized algorithm for estimating the $p$th moment $F_p$ of the frequency vector of a data stream in the general update (turnstile) model to within a multiplicative factor of $1 \pm \epsilon$, for $p > 2$, with high constant…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…
The paper studies a problem of constructing simultaneous likelihood-based confidence sets. We consider a simultaneous multiplier bootstrap procedure for estimating the quantiles of the joint distribution of the likelihood ratio statistics,…
This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on…
We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X,w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
We present an estimator of the covariance matrix $\Sigma$ of random $d$-dimensional vector from an i.i.d. sample of size $n$. Our sole assumption is that this vector satisfies a bounded $L^p-L^2$ moment assumption over its one-dimensional…
In this work, we provide a $(n/m)^{-1/2}$-rate finite sample Berry-Esseen bound for $m$-dependent high-dimensional random vectors over the class of hyper-rectangles. This bound imposes minimal assumptions on the random vectors such as…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential…
Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of…
We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an…
This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and…
In this paper, we construct the wavelet eigenvalue regression methodology in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a low-dimensional $r$-variate ($r \ll p$) fractional…
The Cox proportional hazards model is widely used in survival analysis to model time-to-event data. However, it faces significant computational challenges in the era of large-scale data, particularly when dealing with time-dependent…
Let C = C(l_1, ..., l_n) be the n-dimensional orthogonal cross-polytope whose axes are of length l_1,..., l_n. Subject to the condition \sum l_i^2 = 1, the mean width of C is minimised when l_i = 1/sqrt{n} for every i, and it is maximised…
We propose a conformal prediction method for constructing tight simultaneous prediction intervals for multiple, potentially related, numerical outputs given a single input. This method can be combined with any multi-target regression model…
Based on independent progressively Type-II censored samples from two-parameter Rayleigh distributions with the same location parameter but different scale parameters, the UMVUE and maximum likelihood estimator of $R=P(Y<X)$ are obtained.…
In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…