article · Integers · 2009

Generalized Levinson–Durbin Sequences and Binomial Coefficients

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Abstract

Abstract The 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.

Cite this paper

APA 7

Shaman, P. (2009). Generalized Levinson–Durbin Sequences and Binomial Coefficients. Integers, 9(2). https://doi.org/10.1515/integ.2009.016

MLA 9

Shaman, Paul. “Generalized Levinson–Durbin Sequences and Binomial Coefficients.” Integers, vol. 9, no. 2, 2009, https://doi.org/10.1515/integ.2009.016.

Chicago

Shaman, Paul. 2009. “Generalized Levinson–Durbin Sequences and Binomial Coefficients.” Integers 9 (2). https://doi.org/10.1515/integ.2009.016.

Harvard

Shaman, P. (2009) ‘Generalized Levinson–Durbin Sequences and Binomial Coefficients’, Integers, 9(2). Available at: https://doi.org/10.1515/integ.2009.016.

BibTeX

@article{shaman2009generalized,
  title = {{Generalized Levinson–Durbin Sequences and Binomial Coefficients}},
  author = {Shaman, Paul},
  journal = {Integers},
  volume = {9},
  number = {2},
  year = {2009},
  doi = {10.1515/integ.2009.016}
}

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