A Robust Multiple Correlation Coefficient for the Rank Analysis of Linear Models.

A multiple correlation coefficient is discussed to measure the degree of association between a random variable Y and a set of random variables X sub l, ..., X sub p. The coefficient is defined in terms of weighted Kendalls tau, suitably normalized. It is directly compatible with the rank statistic approach of analyzing linear models in a regression, prediction context. The population parameter equals the classical multiple correlation coefficient if the multivariate normal model holds but would be more robust for departures from this model. Some results are given on the consistency of the sample estimate and on a test for independence. Author