Related papers: Asymptotic Confidence Regions for Density Ridges
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
We introduce an original method of multidimensional ridge penalization in functional local linear regressions. The nonparametric regression of functional data is extended from its multivariate counterpart, and is known to be sensitive to…
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems…
This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition…
The generalization performance of kernel ridge regression (KRR) exhibits a multi-phased pattern that crucially depends on the scaling relationship between the sample size $n$ and the underlying dimension $d$. This phenomenon is due to the…
Statistical methods for metric spaces provide a general and versatile framework for analyzing complex data types. We introduce a novel approach for constructing confidence regions around new predictions from any bagged regression algorithm…
A Two-Stage approach enables researchers to make optimal non-linear predictions via Generalized Ridge Regression using models that contain two or more x-predictor variables and make only realistic minimal assumptions. The optimal regression…
We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…
In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…
We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and…
This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…
The increasing use of vine copulas in high-dimensional settings, where the number of parameters is often of the same order as the sample size, calls for asymptotic theory beyond the traditional fixed-$p$, large-$n$ framework. We establish…
This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…
We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…