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On regression representations of stochastic processes

Author

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  • Rüschendorf, Ludger
  • de Valk, Vincent

Abstract

We construct a.s. nonlinear regression representations of general stochastic processes . As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive method to check, whether these sequences have a monotone (m+1)-block factor representation.

Suggested Citation

  • Rüschendorf, Ludger & de Valk, Vincent, 1993. "On regression representations of stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 183-198, June.
    • Handle: RePEc:eee:spapps:v:46:y:1993:i:2:p:183-198
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    Cited by:

    1. Lamboni, Matieyendou, 2022. "Efficient dependency models: Simulating dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 199-217.
    2. Mai Jan-Frederik & Schenk Steffen & Scherer Matthias, 2015. "Analyzing model robustness via a distortion of the stochastic root: A Dirichlet prior approach," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 177-195, December.
    3. Alessio Sancetta, 2007. "Weak Convergence of Laws on ℝ K with Common Marginals," Journal of Theoretical Probability, Springer, vol. 20(2), pages 371-380, June.
    4. Sancetta, Alessio, 2005. "Distance between nonidentically weakly dependent random vectors and Gaussian random vectors under the bounded Lipschitz metric," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 158-168, December.
    5. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    6. Sancetta, Alessio, 2007. "Nonparametric estimation of distributions with given marginals via Bernstein-Kantorovich polynomials: L1 and pointwise convergence theory," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1376-1390, August.

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