Related papers: A Coefficient of Determination (R2) for Linear Mix…
Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in many scientific fields, ranging from…
Functional linear models are one of the most fundamental tools to assess the relation between two random variables of a functional or scalar nature. This contribution proposes a goodness-of-fit test for the functional linear model with…
We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is…
We go through the many considerations involved in fitting a model to data, using as an example the fit of a straight line to a set of points in a two-dimensional plane. Standard weighted least-squares fitting is only appropriate when there…
Cohort studies employ pairwise measures of association to quantify dependencies among conditions and exposures. To reliably use these measures to draw conclusions about the underlying association strengths requires that the measures be…
The problem of detecting change points in the parameters of a linear regression model with errors and covariates exhibiting heteroscedasticity is considered. Asymptotic results for weighted functionals of the cumulative sum (CUSUM)…
Joint models for longitudinal and time-to-event data are widely used in many disciplines. Nonetheless, existing model comparison criteria do not indicate whether a model adequately fits the data or which components may be misspecified. We…
Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model…
Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Oftentimes, the number of observations is small, and it is thus important to…
We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a…
The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations…
The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…
Variable importance in regression analyses is of considerable interest in a variety of fields. There is no unique method for assessing variable importance. However, a substantial share of the available literature employs Shapley values,…
Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed-effects model for repeated measurements. Using machine learning…
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
The problem of assessing a parametric regression model in the presence of spatial correlation is addressed in this work. For that purpose, a goodness-of-fit test based on a $L_2$-distance comparing a parametric and a nonparametric…
Though data augmentation has become a standard component of deep neural network training, the underlying mechanism behind the effectiveness of these techniques remains poorly understood. In practice, augmentation policies are often chosen…