Related papers: Confidence sets for nonparametric wavelet regressi…
By wavelets approach we estimate densities. Then by means of mean value theorem we establish asymptotic consistency and normality for special divergence measures and construct their consistency bands.
We study the properties of the score confidence set for the local average treatment effect in non and semiparametric instrumental variable models. This confidence set is constructed by inverting a score test based on an estimate of the…
Suppose that one observes pairs $(x_1,Y_1)$, $(x_2,Y_2)$, ..., $(x_n,Y_n)$, where $x_1\le x_2\le ... \le x_n$ are fixed numbers, and $Y_1,Y_2,...,Y_n$ are independent random variables with unknown distributions. The only assumption is that…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…
We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric…
Consider the univariate nonparametric regression model with additive Gaussian noise and the representation of the unknown regression function in terms of a wavelet basis. We propose a shrinkage rule to estimate the wavelet coefficients…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…
We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection…
We discuss non-parametric density estimation and regression for astrophysics problems. In particular, we show how to compute non-parametric confidence intervals for the location and size of peaks of a function. We illustrate these ideas…
The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…
In the present paper, we derive lower bounds for the risk of the nonparametric empirical Bayes estimators. In order to attain the optimal convergence rate, we propose generalization of the linear empirical Bayes estimation method which…
Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
Our confidence set quantifies the statistical uncertainty from data-driven group assignments in grouped panel models. It covers the true group memberships jointly for all units with pre-specified probability and is constructed by inverting…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Predicting sets of outcomes -- instead of unique outcomes -- is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to…
For sparse high-dimensional regression problems, Cox and Battey [1, 9] emphasised the need for confidence sets of models: an enumeration of those small sets of variables that fit the data equivalently well in a suitable statistical sense.…
We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…