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We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…
This article focuses on estimating distribution elements over a high-dimensional binary hypercube from multivariate binary data. A popular approach to this problem, optimizing Walsh basis coefficients, is made more interpretable by an…
New procedures for detecting a change in the cross-sectional mean of panel data are proposed. The procedures rely on estimating nuisance parameters using certain cross-sectional means across panels using a weighted least squares regression.…
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
We consider the problem of detecting a `bump' in the intensity of a Poisson process or in a density. We analyze two types of likelihood ratio based statistics which allow for exact finite sample inference and asymptotically optimal…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…
Achieving a quantum computational advantage regime, and thus providing evidence against the extended Church-Turing thesis, remains one of the key challenges of modern science. Boson sampling seems to be a very promising platform in this…
We experimentally demonstrate a testing strategy for boson samplers that is based on efficiently computable expressions for the output photon counting distributions binned over multiple optical modes. We apply this method to validate boson…
Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect…
Kernel Density Estimation (KDE) is a cornerstone of nonparametric statistics, yet it remains sensitive to bandwidth choice, boundary bias, and computational inefficiency. This study revisits KDE through a principled convolutional framework,…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
In this paper, we provide a statistical testing framework to check whether a random sample splitting in a multi-dimensional space is carried out in a valid way, which could be directly applied to A/B testing and multivariate testing to…
This paper considers distributed M-estimation under heterogeneous distributions among distributed data blocks. A weighted distributed estimator is proposed to improve the efficiency of the standard "Split-And-Conquer" (SaC) estimator for…
The performance and ease of use of deep learning-based binary classifiers have improved significantly in recent years. This has opened up the potential for automating critical inspection tasks, which have traditionally only been trusted to…
Validation of quantum advantage claims in the context of Gaussian Boson Sampling (GBS) currently relies on providing evidence that the experimental samples genuinely follow their corresponding ground truth, i.e., the theoretical model of…
This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original…
Consider a structured dataset of features, such as $\{\textrm{SEX}, \textrm{INCOME}, \textrm{RACE}, \textrm{EXPERIENCE}\}$. A user may want to know where in the feature space observations are concentrated, and where it is sparse or empty.…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…