Related papers: Bias correction and uniform inference for the quan…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in…
We obtain sharp convergence rates, using Dirichlet correctors, for solutions of wave equations in a bounded domain with rapidly oscillating periodic coefficients. The results are used to prove the exact boundary controllability that is…
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation…
Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable…
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions,…
We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
Uniform confidence bands for functions are widely used in empirical analysis. A variety of simple implementation methods (most notably multiplier bootstrap) have been proposed and theoretically justified. However, an implementation over a…
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…
In order to certify performance and safety, feedback control requires precise characterization of sensor errors. In this paper, we provide guarantees on such feedback systems when sensors are characterized by solving a supervised learning…
This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
To derive the auto-covariance function from a sampled and time-limited signal or the cross-covariance function from two such signals, the mean values must be estimated and removed from the signals. If no a priori information about the…
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…