Related Experiment Video
Updated: Jul 3, 2026

Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities
Published on: October 27, 2023
Universal Residuals: A Multivariate Transformation
1( abrock@stat.cmu.edu ) Dept. of Statistics Carnegie Mellon University Pittsburgh, PA 15213-3890, USA.
Abstract:
Rosenblatt's transformation has been used extensively for evaluation of model goodness-of-fit, but it only applies to models whose joint distribution is continuous. In this paper we generalize the transformation so that it applies to arbitrary probability models. The transformation is simple, but has a wide range of possible applications, providing a tool for exploratory data analysis and formal goodness-of-fit testing for a very general class of probability models. The method is demonstrated with specific examples.
More Related Videos
Related Concept Videos
Change of Variables in Multiple Integrals
Residuals and Least-Squares Property
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Transformation
Transformations of Functions II
Transformations of Functions I
Transformations of Functions III
