Adaptive Linear Prediction and Process Order Identification
Part of the
International Centre for Mechanical Sciences
book series (CISM, volume 324)
Adaptive linear predictors are employed to provide solutions to problems ranging from adaptive source coding to autoregressive (AR) spectral estimation. In such applications, an adaptive linear predictor is realized by a linear combination of a finite number, M, of the observations immediately preceding each sample to be predicted, where the coefficients defining the predictor are “adapted to”, or estimated on the basis of, the preceding N + M observations in an attempt to continually optimize the predictor’s performance. This performance is thus inevitably dictated by the predictor's order, M, and the length of its learning period, N.
We formulate the adaptive linear predictor’s MSE performance in a series of theorems, with and without the Gaussian assumption, under the hypotheses that its coefficients are derived from either the (single) observation sequence to be predicted (dependent case), or a second, statistically independent realization (independent case). The established theory on adaptive linear predictor performance and order selection is reviewed, including the works of Davisson (Gaussian, dependent case), and Akaike (AR, independent case). Results predicated upon the independent case hypothesis (e.g., Akaike’s FPE procedure) are shown to incur substantial error under the dependent case conditions prevalent in typical adaptive prediction environments. Similarly, theories based on the Gaussian assumption are found to suffer a loss in accuracy which is proportional to the deviation, of the probability law governing the process in question, from the normal distribution.
We develop a theory on the performance of, and an optimal order selection criterion for, an adaptive linear predictor which is applicable under the dependent case, in environments where the Gaussian assumption is not necessarily justifiable.
KeywordsLess Mean Square Independent Case Linear Minimum Mean Square Error Gaussian Assumption Dependent Case
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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