Related papers: Nonparametric Smoothing of Directional and Axial D…

We develop inference and testing procedures for conditional dispersion and skewness in a nonparametric regression setup based on statistical depth functions. The methods developed can be applied in situations, where the response is…

For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…

The von Mises-Fisher family is a parametric family of distributions on the surface of the unit ball, summarised by a concentration parameter and a mean direction. As a quasi-Bayesian prior, the von Mises-Fisher distribution is a convenient…

In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for…

In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…

We consider the fundamental problem of learning linear predictors (i.e., separable datasets with zero margin) using neural networks with gradient flow or gradient descent. Under the assumption of spherically symmetric data distribution, we…

We present a new theoretical perspective of data noising in recurrent neural network language models (Xie et al., 2017). We show that each variant of data noising is an instance of Bayesian recurrent neural networks with a particular…

We address the goal of conducting inference about a smooth finite-dimensional parameter by utilizing individual-level data from various independent sources. Recent advancements have led to the development of a comprehensive theory capable…

In 2020, two novel distributions for the analysis of directional data were introduced: the spherical Cauchy distribution and the Poisson kernel-based distribution. This paper provides a detailed exploration of both distributions within…

Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…

Motivated by investigating spatio-temporal patterns of the distribution of continuous variables, we consider describing the conditional distribution function of the response variable incorporating spatio-temporal components given…

To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…

We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…

We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional…

The modelling of data on a spherical surface requires the consideration of directional probability distributions. To model asymmetrically distributed data on a three-dimensional sphere, Kent distributions are often used. The moment…