Related papers: Uniform estimation of a signal based on inhomogene…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…
In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test…
Researchers may perform regressions using a sketch of data of size $m$ instead of the full sample of size $n$ for a variety of reasons. This paper considers the case when the regression errors do not have constant variance and…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…
This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…
Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…
Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
We introduce a new nonparametric framework for classification problems in the presence of missing data. The key aspect of our framework is that the regression function decomposes into an anova-type sum of orthogonal functions, of which some…
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and strong uniform consistency are derived…