Related papers: Nonparametric regression with homogeneous group te…

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…

Recently, there has been great interest in estimating the conditional average treatment effect using flexible machine learning methods. However, in practice, investigators often have working hypotheses about effect heterogeneity across…

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…

When the response mechanism is believed to be not missing at random (NMAR), a valid analysis requires stronger assumptions on the response mechanism than standard statistical methods would otherwise require. Semiparametric estimators have…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

We propose a compressed sensing-based testing approach with a practical measurement design and a tuning-free and noise-robust algorithm for detecting infected persons. Compressed sensing results can be used to provably detect a small number…

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

Extreme value theory has constructed asymptotic properties of the sample maximum. This study concerns probability distribution estimation of the sample maximum. The traditional approach is parametric fitting to the limiting distribution --…

Many massive data are assembled through collections of information of a large number of individuals in a population. The analysis of such data, especially in the aspect of individualized inferences and solutions, has the potential to create…

We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…

A combinatorial analysis of the false alarm (FA) and misdetection (MD) probabilities of non-adaptive group testing with sparse pooling graphs is developed. The analysis targets the combinatorial orthogonal matching pursuit and definite…

We propose a new method for studying environments with unobserved individual heterogeneity. Based on model-implied pairwise inequalities, the method classifies individuals in the sample into groups defined by discrete unobserved…

Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…

Matching a nonprobability sample to a probability sample is one strategy both for selecting the nonprobability units and for weighting them. This approach has been employed in the past to select subsamples of persons from a large panel of…

In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…

Supervised learning under measurement constraints is a common challenge in statistical and machine learning. In many applications, despite extensive design points, acquiring responses for all points is often impractical due to resource…

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.…

Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…