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Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
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…
This work focuses on angular values of nonautonomous dynamical systems which have been introduced for general random and (non)autonomous dynamical systems in a previous publication [W.-J. Beyn, G. Froyland, and T. H\"uls, SIAM J. Appl. Dyn.…
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in…
Galactic rotation curves are crucial for understanding the distribution of mass in galaxies. Despite advances in precision observations, there are discrepancies between the inferred mass from luminosity and the observed rotational…
Uniform asymptotic confidence bands for a multivariate regression function in an inverse regression model with a convolution-type operator are constructed. The results are derived using strong approximation methods and a limit theorem for…
The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
Analysis of geospatial data has traditionally been model-based, with a mean model, customarily specified as a linear regression on the covariates, and a covariance model, encoding the spatial dependence. We relax the strong assumption of…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
The multivariate adaptive regression spline (MARS) is one of the popular estimation methods for nonparametric multivariate regressions. However, as MARS is based on marginal splines, to incorporate interactions of covariates, products of…
A statistical predictive model in which a high-dimensional time-series regenerates at the end of each day is used to model road traffic. Due to the regeneration, prediction is based on a daily modeling using a vector autoregressive model…
This paper presents the recurrent estimation of distributions (RED) for modeling real-valued data in a semiparametric fashion. RED models make two novel uses of recurrent neural networks (RNNs) for density estimation of general real-valued…
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
A permanently increasing number of on-board automotive control systems requires new approaches to their digital mapping that improves functionality in terms of adaptability and robustness as well as enables their easier on-line software…
This paper develops non-parametric rotation invariant CUSUMs suited to the detection of changes in the mean direction as well as changes in the concentration parameter of angular data. The properties of the CUSUMs are illustrated by…
The recurrent neural network and its variants have shown great success in processing sequences in recent years. However, this deep neural network has not aroused much attention in anomaly detection through predictively process monitoring.…
This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to…