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This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…
Recent advances in machine learning have been achieved by using overparametrized models trained until near interpolation of the training data. It was shown, e.g., through the double descent phenomenon, that the number of parameters is a…
The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A…
In Selk and Gertheiss (2022) a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, thus both…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
We study estimation and prediction of Gaussian processes with covariance model belonging to the generalized Cauchy (GC) family, under fixed domain asymptotics. Gaussian processes with this kind of covariance function provide separate…
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…
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…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…
We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…
This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…