Data Transformation (statistics) - Transformations For Multivariate Data

Transformations For Multivariate Data

Univariate functions can be applied point-wise to multivariate data to modify their marginal distributions. It is also possible to modify some attributes of a multivariate distribution using an appropriately constructed transformation. For example, when working with time series and other types of sequential data, it is common to difference the data to improve stationarity. If data are observed as random vectors X_i with covariance matrix Σ, a linear transformation can be used to decorrelate the data. To do this, use the Cholesky decomposition to express Σ = A A'. Then the transformed vector Y_i = A−1X_i has the identity matrix as its covariance matrix.