Related papers: Does Regression Approximate the Influence of the C…
A simple test is proposed for examining the correctness of a given completely specified response function against unspecified general alternatives in the context of univariate regression. The usual diagnostic tools based on residuals plots…
We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…
Measurement error in the covariate of main interest (e.g. the exposure variable, or the risk factor) is common in epidemiologic and health studies. It can effect the relative risk estimator or other types of coefficients derived from the…
For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…
Random effects are a flexible addition to statistical models to capture structural heterogeneity in the data, such as spatial dependencies, individual differences, temporal dependencies, or non-linear effects. Testing for the presence (or…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
We propose an empirical likelihood test that is able to test the goodness of fit of a class of parametric and semi-parametric multiresponse regression models. The class includes as special cases fully parametric models; semi-parametric…
Meta-regression is often used to form hypotheses about what is associated with heterogeneity in a meta-analysis and to estimate the extent to which effects can vary between cohorts and other distinguishing factors. However, study-level…
This article focuses on measurement error in covariates in regression analyses in which the aim is to estimate the association between one or more covariates and an outcome, adjusting for confounding. Error in covariate measurements, if…
In the field of modeling, the word validation refers to simple comparisons between model outputs and experimental data. Usually, this comparison constitutes plotting the model results against data on the same axes to provide a visual…
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
Measurement error arises through a variety of mechanisms. A rich literature exists on the bias introduced by covariate measurement error and on methods of analysis to address this bias. By comparison, less attention has been given to errors…
Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions $f : \mathcal{X} \rightarrow \mathbb{R}$). These models perform better (with respect to $L^2$ loss) and are…
Adjusting for covariates is a well established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study there may be different adjustment…
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…
Reliability of machine learning evaluation -- the consistency of observed evaluation scores across replicated model training runs -- is affected by several sources of nondeterminism which can be regarded as measurement noise. Current…
Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In…
Numerical predictions of quantities of interest measured within physical systems rely on the use of mathematical models that should be validated, or at best, not invalidated. Model validation usually involves the comparison of experimental…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…