Computing exact score vectors for linear Gaussian state space models

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1 Citation (Scopus)


A recursive formula for computing the exact value of score vectors is proposed for a general form of the linear Gaussian state space model, which is more desirable than approximate values in some statistical analyses. Unlike most extant methods, our formula calculates all components of the score vector simultaneously. This approach significantly simplifies its programing, in particular, with some matrix-oriented programing languages, such as MATLAB. We also consider a way of handling initial conditions that depend on unknown parameters. This issue has not yet been explicitly addressed in the existing literature in the context of exact score computing for a general case, such as the one that we consider in this paper. It is also shown that our formula is especially useful for calculating score tests with an outer product of gradient asymptotic covariance matrix estimator.

Original languageEnglish
Pages (from-to)2313-2326
Number of pages14
JournalCommunications in Statistics: Simulation and Computation
Issue number8
Publication statusPublished - 2021


  • 15A99
  • 60G35
  • 62H15
  • Initial condition
  • Recursive formula
  • Score test
  • Score vector
  • State space model

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation


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