The Application of Mahalanobis Distance Based on the Ridge Estimation in Data with Multicollinearity

Multicollinearity is often among variables in the multi-dimensional data, which will affect the performence of parameter estimation, make parameters extremely sensitive on slight variable's perturbation. The robustness of mahalanobis distance calculation must be decreased due to the existence of multicollinearity. This paper presents a new measuring scale function-ridge mahalanobis distance, which is based on the ridge estimation, by adding the ridge disturbance term to the sample covariance matrix, the effect of multicollinearity can well be reduced. And put forward a new method to determine the ridge parameters through the analysis of the influence of multicollinearity to sample covariance matrix.