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Kalman filter variants in the closed skew normal setting

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  • Rezaie, Javad
  • Eidsvik, Jo

Abstract

The filtering problem (or the dynamic data assimilation problem) is studied for linear and nonlinear systems with continuous state space and over discrete time steps. Filtering approaches based on the conjugate closed skewed normal probability density function are presented. This distribution allows additional flexibility over the usual Gaussian approximations. With linear dynamic systems the filtering problem can be solved in analytical form using expressions for the closed skew normal distribution. With nonlinear dynamic systems an ensemble-based version is proposed for fitting a closed skew normal distribution at each updating step. Numerical examples discuss various special cases of the methods.

Suggested Citation

  • Rezaie, Javad & Eidsvik, Jo, 2014. "Kalman filter variants in the closed skew normal setting," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 1-14.
    • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:1-14
    DOI: 10.1016/j.csda.2014.01.014
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    References listed on IDEAS

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    1. Flecher, C. & Naveau, P. & Allard, D., 2009. "Estimating the closed skew-normal distribution parameters using weighted moments," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1977-1984, October.
    2. Gupta, Arjun K. & González-Farías, Graciela & Domínguez-Molina, J. Armando, 2004. "A multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 181-190, April.
    3. Omid Karimi & Mohsen Mohammadzadeh, 2012. "Bayesian spatial regression models with closed skew normal correlated errors and missing observations," Statistical Papers, Springer, vol. 53(1), pages 205-218, February.
    4. Naveau, Philippe & Genton, Marc G. & Shen, Xilin, 2005. "A skewed Kalman filter," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 382-400, June.
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    Cited by:

    1. Gaygysyz Guljanov & Willi Mutschler & Mark Trede, 2022. "Pruned Skewed Kalman Filter and Smoother: With Application to the Yield Curve," CQE Working Papers 10122, Center for Quantitative Economics (CQE), University of Muenster.
    2. Reinaldo B. Arellano-Valle & Javier E. Contreras-Reyes & Freddy O. López Quintero & Abel Valdebenito, 2019. "A skew-normal dynamic linear model and Bayesian forecasting," Computational Statistics, Springer, vol. 34(3), pages 1055-1085, September.

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