Related papers: Sampling from a couple of positively correlated bi…
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…
We propose an estimation approach to analyse correlated functional data which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
We consider the variable selection problem in linear regression. Suppose that we have a set of random variables $X_1,...,X_m,Y,\epsilon$ such that $Y=\sum_{k\in \pi}\alpha_kX_k+\epsilon$ with $\pi\subseteq \{1,...,m\}$ and $\alpha_k\in…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
Control variables are included in regression analyses to estimate the causal effect of a treatment on an outcome. In this paper, we argue that the estimated effect sizes of controls are unlikely to have a causal interpretation themselves,…
This paper shows that the degree of approximate multicollinearity in a linear regression model increases simply by including independent variables, even if these are not highly linearly related. In the current situation where it is…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Sampling from multivariate normal distributions, subjected to a variety of restrictions, is a problem that is recurrent in statistics and computing. In the present work, we demonstrate a general framework to efficiently sample a…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…