Related papers: Constrained High Dimensional Statistical Inference

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…

A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…

There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this…

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection…

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…

Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…

Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…

Missing data are frequently encountered in high-dimensional problems, but they are usually difficult to deal with using standard algorithms, such as the expectation-maximization (EM) algorithm and its variants. To tackle this difficulty,…

An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…

In this paper, we address the problem of conducting statistical inference in settings involving large-scale data that may be high-dimensional and contaminated by outliers. The high volume and dimensionality of the data require distributed…

We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…

This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…

Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…

This paper revisits the simple, but empirically salient, problem of inference on a real-valued parameter that is partially identified through upper and lower bounds with asymptotically normal estimators. A simple confidence interval is…

High complexity models are notorious in machine learning for overfitting, a phenomenon in which models well represent data but fail to generalize an underlying data generating process. A typical procedure for circumventing overfitting…

High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…

In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…