Lack-of-fit Testing for Polynomial Regression Models Without Replications

Testing lack of fit of regression models under heteroscedasticity

A test is proposed for assessing the lack of fit of heteroscedastic nonlinear regression models that is based on comparison of nonparametric kernel and parametric fits. A data-driven method is proposed for bandwidth selection using the parametric null model asymptotically optimal bandwidth which leads to a test that has a limiting normal distribution under the null hypothesis and is consistent ...

Testing Lack-of-fit of Parametric Regression Models Using Nonparametric Regression Techniques

Data-driven lack-of-fit tests are derived for parametric regression models using fit comparison statistics that are based on nonparametric linear smoothers. The tests are applicable to settings where the usual bandwidth/smoothing parameter asymptotics apply to the null model, which includes testing for nonlinear models and some linear models. Large sample distribution theory is established for ...

Testing for lack of fit in inverse regression – with applications to biophotonic imaging

We propose two test statistics for use in inverse regression problems Y = Kθ + , where K is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations Y for the function θ are available. Both test statistics have a counterpart in classical hypothesis testing, where they are called the order selection test and the data-driven Neyman smooth test. We als...

Bayesian Polynomial Regression Models to Fit Multiple Genetic Models for Quantitative Traits.

We present a coherent Bayesian framework for selection of the most likely model from the five genetic models (genotypic, additive, dominant, co-dominant, and recessive) commonly used in genetic association studies. The approach uses a polynomial parameterization of genetic data to simultaneously fit the five models and save computations. We provide a closed-form expression of the marginal likel...

Empirical L2-distance lack-of-fit tests for Tobit regression models