Related papers: A Theory of Nonparametric Covariance Function Esti…

Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…

Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…

We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…

We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$, estimation and inference is…

In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In…

We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…

We consider the convolution model where i.i.d. random variables $X_i$ having unknown density $f$ are observed with additive i.i.d. noise, independent of the $X$'s. We assume that the density $f$ belongs to either a Sobolev class or a class…

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…

In this work, we consider the problem of bounding the values of a covariance function corresponding to a continuous-time stationary stochastic process or signal. Specifically, for two signals whose covariance functions agree on a finite…

Recent advances in deep learning have achieved impressive gains in classification accuracy on a variety of types of data, including images and text. Despite these gains, however, concerns have been raised about the calibration, robustness,…

In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…

Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt…

Doubly robust estimators with cross-fitting have gained popularity in causal inference due to their favorable structure-agnostic error guarantees. However, when additional structure, such as H\"{o}lder smoothness, is available then more…

Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…

Traditional survival models often rely on restrictive assumptions such as proportional hazards or instantaneous effects of time-varying covariates on the hazard function, which limit their applicability in real-world settings. We consider…

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

This paper studies the finite sample performance of the flexible estimation approach of Farrell, Liang, and Misra (2021a), who propose to use deep learning for the estimation of heterogeneous parameters in economic models, in the context of…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…