Generalized Levinson–Durbin Sequences and Binomial Coefficients
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AbstractThe Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson–Durbin sequence is also defined, and we note that binomial coefficients constitute a special case of such a sequence. Generalized Levinson–Durbin sequences obey formulas which generalize relations satisfied by binomial coefficients. Some of these results are extended to vector stationary processes.
2002 ◽
Vol 47
(8)
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pp. 1351-1356
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1966 ◽
Vol 14
(3)
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pp. 302-308
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1994 ◽
Vol 39
(8)
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pp. 1685-1689
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2019 ◽
Vol 28
(1)
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pp. 145-152
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