A Method of Bivariate Trimming for Robust Estimation of the Correlation Coefficient

SUMMARY It is proposed that bivariate data should be trimmed of those points which define the convex hull, for robust estimation of the product-moment correlation coefficient. Properties of this method are examined by a Monte Carlo investigation. Other applications are mentioned. THE product-moment correlation coefficient, like many other parametric estimators, is sensitive to outliers and disturbances in the tails of the bivariate distribution of quantitative variables. For this reason there is much to recommend the routine application of a trimming procedure before this statistic is calculated. Previous authors, e.g. Nath (1971), have investigated what may be termed a rectangular trimming procedure: that is, each distribution independently is truncated in each tail. While this method has the virtue of simplicity, there may be certain objections to its use. Firstly, it takes no account of the multivariate structure of the data. This may well be important particularly if the truncated sample will be used in more complex multivariate procedures. Secondly, the rectangular trimmed product-moment correlation coefficient is almost certain to be biased toward zero as an estimate of the population correlation. Nath (1971) gives an example of a correlation of 079 which reduced to 065 on single truncation of either distribution resulting in 23 per cent of the sample being eliminated. A bias correction may be calculated assuming a bivariate normal distribution, but is computationally tedious, even though Dyer (1973) has proposed a method avoiding complex iteration.