Some Useful Techniques for High-Dimensional Statistics

High-dimensional statistics are used when n<5p, where n is the sample size and p is the number of predictors. Useful techniques include (a) the use of a sparse fitted model, (b) use of principal component analysis for dimension reduction, (c) use of alternative multivariate dispersion estimators instead of the sample covariance matrix, (d) eliminate weak predictors, and (e) stack low-dimensional estimators into a vector. Some variants and theory for these techniques will be given or reviewed.