Related papers: Nonparametric Spherical Regression Using Diffeomor…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…
The `Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a…
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,…
A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true…
In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
In oceanography, modeling wave fields requires the use of statistical tools capable of handling the circular nature of the {data measurements}. An important issue in ocean wave analysis is the study of height and direction waves, being…
Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
Identifying an appropriate covariance function is one of the primary interests in spatial and spatio-temporal statistics because it allows researchers to analyze the dependence structure of the random process. For this purpose, spatial…
Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…