相关论文: Regression Models for Directional Data Based on No…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…
Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and…
Graph Neural Networks (GNNs) have recently been explored as surrogate models for numerical simulations. While their applications in computational fluid dynamics have been investigated, little attention has been given to structural problems,…
Histogram-valued variables are a particular kind of variables studied in Symbolic Data Analysis where to each entity under analysis corresponds a distribution that may be represented by a histogram or by a quantile function. Linear…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…
Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…
Many scientific and engineering applications require fitting regression models that are nonlinear in the parameters. Advances in computer hardware and software in recent decades have made it easier to fit such models. Relative to fitting…
Future galaxy clustering surveys will probe small scales where non-linearities become important. Since the number of modes accessible on intermediate to small scales is very high, having a precise model at these scales is important…
This paper introduces a novel regression model designed for angular response variables with linear predictors, utilizing a generalized M\"{o}bius transformation to define the regression curve. By mapping the real axis to the circle, the…
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 are presenting a method of linear regression based on Gram-Schmidt orthogonal projection that does not compute a pseudo-inverse matrix. This is useful when we want to make several regressions with random data vectors for simulation…
We propose new small-sphere distributional families for modeling multivariate directional data on $(\mathbb{S}^{p-1})^K$ for $p \ge 3$ and $K \ge 1$. In a special case of univariate directions in $\Re^3$, the new densities model random…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
This paper suggests parametrically transformed nested error regression models (TNERM), which transform the data flexibly to follow the normal linear mixed regression. We provide a procedure for estimating consistently the parameters of the…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Using a statistical model-based data generation, we develop an experimental setup for the evaluation of neural networks (NNs). The setup helps to benchmark a set of NNs vis-a-vis minimum-mean-square-error (MMSE) performance bounds. This…