LOW-RANK ESTIMATION OF HIGHER-ORDER STATISTICS

Low-rank estimators for higher order statistics are considered in this paper. The bias-variance tradeoff is analyzed for low-rank estimators of higher order statistics using a tensor product formulation for the moments and cumulants. In general, the low-rank estimators have a lar ger bias and smaller variance than the corresponding full-rank estimat or, and the mean-squared error can be significantly smaller. This make s the low-rank estimators extremely useful for signal processing algor ithms based on sample estimates of the higher order statistics. The lo w-rank estimators also offer considerable reductions in the computatio nal complexity of such algorithms. The design of subspaces to optimize the tradeoffs between bias, variance, and computation is discussed, a nd a noisy input, noisy output system identification problem is used t o illustrate the results.