Related papers: Nonparametric regression for locally stationary ra…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
This paper considers a linear regression model with an endogenous regressor which arises from a nonlinear transformation of a latent variable. It is shown that the corresponding coefficient can be consistently estimated without external…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
We discuss local linear smooth backfitting for additive non-parametric models. This procedure is well known for achieving optimal convergence rates under appropriate smoothness conditions. In particular, it allows for the estimation of each…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
In this paper, we attempt to shed light on a new class of nonstationary random fields which exhibit, what we call, local invariant nonstationarity. We argue that the local invariant property has a special interaction with a new generalized…
While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…
Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations…
A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in $\mathbb{R}^\infty$ and related approximation properties are investigated using the popular…
Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…
We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…
We study the asymptotic behaviour of least squares estimators in regression models for long-range dependent random fields observed on spheres. The least squares estimator can be given as a weighted functional of long-range dependent random…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
In this paper, we built a new nonparametric regression estimator with the local linear method by using the mean squared relative error as a loss function when the data are subject to random right censoring. We establish the uniform almost…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
We develop an asymptotic limit theory for nonparametric estimation of the noise covariance kernel in linear parabolic stochastic partial differential equations (SPDEs) with additive colored noise, using space-time infill asymptotics. The…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…