### Abstract

Koopman and Shephard (1992). [1] and Segal and Weinstein (1989). [4] propose a formula for calculating the exact score vector for a general form of linear Gaussian state space models. However, for applying their method, one needs to calculate the derivatives of functions with respect to vectors and matrices, which can be intractable in many practical cases. Koopman and Shephard (1992). [1] derive its explicit expression only for a particular case. In this note, we complement Koopman and Shephard (1992). [1] and Segal and Weinstein. [4] by deriving an explicit vector expression of the exact score vector for the general form of linear Gaussian state space models.

Original language | English |
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Pages (from-to) | 69-74 |

Number of pages | 6 |

Journal | Statistical Methodology |

Volume | 13 |

DOIs | |

Publication status | Published - 2013 Jul |

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### Keywords

- Score vector
- State space model

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

**Explicit vector expression of exact score for time series models in state space form.** / Nagakura, Daisuke.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Explicit vector expression of exact score for time series models in state space form

AU - Nagakura, Daisuke

PY - 2013/7

Y1 - 2013/7

N2 - Koopman and Shephard (1992). [1] and Segal and Weinstein (1989). [4] propose a formula for calculating the exact score vector for a general form of linear Gaussian state space models. However, for applying their method, one needs to calculate the derivatives of functions with respect to vectors and matrices, which can be intractable in many practical cases. Koopman and Shephard (1992). [1] derive its explicit expression only for a particular case. In this note, we complement Koopman and Shephard (1992). [1] and Segal and Weinstein. [4] by deriving an explicit vector expression of the exact score vector for the general form of linear Gaussian state space models.

AB - Koopman and Shephard (1992). [1] and Segal and Weinstein (1989). [4] propose a formula for calculating the exact score vector for a general form of linear Gaussian state space models. However, for applying their method, one needs to calculate the derivatives of functions with respect to vectors and matrices, which can be intractable in many practical cases. Koopman and Shephard (1992). [1] derive its explicit expression only for a particular case. In this note, we complement Koopman and Shephard (1992). [1] and Segal and Weinstein. [4] by deriving an explicit vector expression of the exact score vector for the general form of linear Gaussian state space models.

KW - Score vector

KW - State space model

UR - http://www.scopus.com/inward/record.url?scp=84874414427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874414427&partnerID=8YFLogxK

U2 - 10.1016/j.stamet.2013.01.003

DO - 10.1016/j.stamet.2013.01.003

M3 - Article

AN - SCOPUS:84874414427

VL - 13

SP - 69

EP - 74

JO - Statistical Methodology

JF - Statistical Methodology

SN - 1572-3127

ER -