Correlation Tests for Non-Linear Alternatives
- 1 January 1993
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 55 (2) , 541-548
- https://doi.org/10.1111/j.2517-6161.1993.tb01922.x
Abstract
A new class of statistics for detecting association between two variables is proposed. The statistics improve on traditional correlation coefficients by being sensitive to U‐shaped and other non‐linear relationships between the variables. If both variables are one dimensional, they can be simply defined in terms of ranks, so that their null distributions can in principle be tabulated. Asymptotic discrimination of order n−1/2 is obtained for any alternative of a continuous functional relationship between the variables. Power against trend alternatives is investigated by simulation.This publication has 2 references indexed in Scilit:
- Random association of symmetric arraysStochastic Analysis and Applications, 1986
- Mantel's space-time clustering statistic: computing higher moments and a comparison of various data transformsJournal of Statistical Computation and Simulation, 1978