Related papers: A Simple Lack-of-Fit Test for Regression Models
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…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
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…
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…
We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…
Within the nonparametric regression model with unknown regression function $l$ and independent, symmetric errors, a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis $l=0$ against a…
Assessing model adequacy is a crucial step in regression analysis, ensuring the validity of statistical inferences. For Generalized Functional Linear Models (GFLMs), which are widely used for modeling relationships between scalar responses…
We propose a novel framework of the model specification test in regression using unlabeled test data. In many cases, we have conducted statistical inferences based on the assumption that we can correctly specify a model. However, it is…
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…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…
Regression experts consistently recommend plotting residuals for model diagnosis, despite the availability of many numerical hypothesis test procedures designed to use residuals to assess problems with a model fit. Here we provide evidence…
In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models…
We introduce equivalence testing procedures for linear regression analyses. Such tests can be very useful for confirming the lack of a meaningful association between a continuous outcome and a continuous or binary predictor. Specifically,…
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…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…
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…