Marked Empirical Process Research Articles

ON TESTING THE GOODNESS-OF-FIT OF NONLINEAR HETEROSCEDASTIC REGRESSION MODELS

For testing the adequacy of a parametric model in regression, various test statistics can be constructed on the basis of a marked empirical process of residuals. By using a discretized version of the decomposition of the corresponding Gaussian limiting process into its principal components, we obtain a test statistic with an asymptotic chi-squared distribution under the null hypothesis. We investigate the consistency of this test statistic and of the estimators needed to compute it. Numerical experiments indicate that the distributional approximations already work for small to moderate sample sizes and reveal that the test has good power properties against a variety of alternatives. The test has a simple implementation. We present an application to a real-data example for testing the adequacy of a possible heteroscedastic exponential model.

Nonparametric model checks in censored regression

Let M be a parametric model for an unknown regression function m. In order to check the validity of M, i.e., to test for m ∈ M, it is known that optinal tests should be based on the empirical process of the regressors marked by the residuals. In this paper we extend the methodology to censored regression. The asymptotic distribution of the underlying marked empirical process in provided. The Wild Bootstrap, appropriately modified to account for censhorship, provides distributional approximations. The method is applied to simulated data sets as well as tto the Stanford Heart Transplant Data.

Goodness-of-fit tests for nonlinear heteroscedastic regression models

This paper is devoted to goodness-of-fit tests for parametric possibly nonlinear heteroscedastic regression models. The test statistic is constructed using a marked empirical process based on residuals. We investigate the consistency of this test statistic and of the estimators needed to compute it. We illustrate our results with numerical experiments and comparisons to other tests.

Nonparametric model checks for regression

In this paper we study a marked empirical process based on residuals. Results on its large-sample behavior may be used to provide nonparametric full-model checks for regression. Their decomposition into principal components gives new insight into the question: which kind of departure from a hypothetical model may be well detected by residual-based goodness-of-fit methods? The work also contains a small simulation study on straight-line regression.