Related papers: Parameter estimation in linear regression driven b…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
A partially linear probit model for spatially dependent data is considered. A triangular array setting is used to cover various patterns of spatial data. Conditional spatial heteroscedasticity and non-identically distributed observations…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
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…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
A local linear kernel estimator of the regression function x\mapsto g(x):=E[Y_i|X_i=x], x\in R^d, of a stationary (d+1)-dimensional spatial process {(Y_i,X_i),i\in Z^N} observed over a rectangular domain of the form I_n:={i=(i_1,...,i_N)\in…
In this paper, we consider a linear regression model with AR(p) error terms with the assumption that the error terms have a t distribution as a heavy tailed alternative to the normal distribution. We obtain the estimators for the model…
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…
Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. This paper addresses the use of a…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
This paper proposes a novel method to estimate parameters in a logistic regression model. After obtaining the estimators, their asymptotic properties are rigorously investigated.
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning…
We present a statistically and computationally efficient spectral-domain maximum-likelihood procedure to solve for the structure of Gaussian spatial random fields within the Matern covariance hyperclass. For univariate, stationary, and…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…
This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…