Related papers: Generalized Ridge Regression: Applications to Nono…
We consider standard gradient descent, gradient flow and conjugate gradients as iterative algorithms for minimising a penalised ridge criterion in linear regression. While it is well known that conjugate gradients exhibit fast numerical…
We propose a random-effects approach to missing values for generalized linear mixed model (GLMM) analysis. The method converts a GLMM with missing covariates to another GLMM without missing covariates. The standard GLMM analysis tools for…
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 generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They…
We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional…
Several studies have focused on the Realized Range Volatility, an estimator of the quadratic variation of financial prices, taking into account the impact of microstructure noise and jumps. However, none has considered direct modeling and…
We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the…
A conventional wisdom in statistical learning is that large models require strong regularization to prevent overfitting. Here we show that this rule can be violated by linear regression in the underdetermined $n\ll p$ situation under…
This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
Two popular approaches for relating correlated measurements of a non-Gaussian response variable to a set of predictors are to fit a marginal model using generalized estimating equations and to fit a generalized linear mixed model by…
Induction benefits from useful priors. Penalized regression approaches, like ridge regression, shrink weights toward zero but zero association is usually not a sensible prior. Inspired by simple and robust decision heuristics humans use, we…
A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…
Most of the recent results in polynomial functional regression have been focused on an in-depth exploration of single-parameter regularization schemes. In contrast, in this study we go beyond that framework by introducing an algorithm for…
Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…
A method for estimating nonlinear regression errors and their distributions without performing regression is presented. Assuming continuity of the modeling function the variance is given in terms of conditional probabilities extracted from…
It has been some time since interval-valued linear regression was investigated. In this paper, we focus on linear regression for interval-valued data within the framework of random sets. The model we propose generalizes a series of existing…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
When modelling censored observations, a typical approach in current regression methods is to use a censored-Gaussian (i.e. Tobit) model to describe the conditional output distribution. In this paper, as in the case of missing data, we argue…
Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the…
The reparameterization gradient has become a widely used method to obtain Monte Carlo gradients to optimize the variational objective. However, this technique does not easily apply to commonly used distributions such as beta or gamma…