The Half-Half Plot

Abstract

The Half-Half (HH) plot is a new graphical method to investigate qualitatively the shape of a regression curve. The empirical HH-plot counts observations in the lower and upper quarter of a strip that moves horizontally over the scatterplot. The plot displays jumps clearly and reveals further features of the regression curve. We prove a functional central limit theorem for the empirical HH-plot, with rate of convergence . In a simulation study, the good performance of the plot is demonstrated. The method is also applied to two case studies. The proofs and one more case study are deferred to a supplement, which is available online.

Keywords:

• Data analysis
• Functional central limit theorem
• Graphical methods
• Jump detection
• Nonparametric regression.

ACKNOWLEDGMENTS

We thank Irène Gijbels for providing the Prague temperature data and Otilia Boldea and Günther Sawitzki for stimulating discussions. Furthermore, we are grateful to the editor, the associate editor, and three referees for a careful reading of the manuscript and for constructive criticism that led to significant improvements.