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Low-rank estimation of higher order statistics

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3 Author(s)
Andre, T.F. ; Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI, USA ; Nowak, R.D. ; Van Veen, B.D.

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 larger bias and smaller variance than the corresponding full-rank estimator, and the mean-squared error can be significantly smaller. This makes the low-rank estimators extremely useful for signal processing algorithms based on sample estimates of the higher order statistics. The low-rank estimators also offer considerable reductions in the computational complexity of such algorithms. The design of subspaces to optimize the tradeoffs between bias, variance, and computation is discussed, and a noisy input, noisy output system identification problem is used to illustrate the results

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Signal Processing, IEEE Transactions on  (Volume:45 ,  Issue: 3 )