Related papers: A maximal inequality for local empirical processes…
This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal…
We develop a wavelet like representation of functions in $L^p(\mathbb{R})$ based on their Fourier--Hermite coefficients; i.e., we describe an expansion of such functions where the local behavior of the terms characterize completely the…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any…
We consider the nonparametric estimation of the density function of weakly and strongly dependent processes with noisy observations. We show that in the ordinary smooth case the optimal bandwidth choice can be influenced by long range…
In this paper, we perform deep neural networks for learning $\psi$-weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association,$\cdots$ and the setting considered here…
We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…
In this article, we consider flexible seasonal time series models which consist of a common trend function over periods and additive individual trend (seasonal effect) functions. The consistency and asymptotic normality of the local linear…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
The level set estimation problem seeks to find all points in a domain ${\cal X}$ where the value of an unknown function $f:{\cal X}\rightarrow \mathbb{R}$ exceeds a threshold $\alpha$. The estimation is based on noisy function evaluations…
A local linear kernel estimator of the regression function x\mapsto g(x):=E[Y_i|X_i=x], x\in R^d, of a stationary (d+1)-dimensional spatial process {(Y_i,X_i),i\in Z^N} observed over a rectangular domain of the form I_n:={i=(i_1,...,i_N)\in…
We consider best approximation problems in a nonlinear subset $\mathcal{M}$ of a Banach space of functions $(\mathcal{V},\|\bullet\|)$. The norm is assumed to be a generalization of the $L^2$-norm for which only a weighted Monte Carlo…
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…
Estimating the spectral density function $f(w)$ for some $w\in [-\pi, \pi]$ has been traditionally performed by kernel smoothing the periodogram and related techniques. Kernel smoothing is tantamount to local averaging, i.e., approximating…
We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the…
Predictive process monitoring focuses on forecasting future states of ongoing process executions, such as predicting the outcome of a particular case. In recent years, the application of machine learning models in this domain has garnered…
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of…