### Abstract

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 language | English |
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Journal | Communications in Statistics: Simulation and Computation |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Modelling and Simulation

### Cite this

**Computing exact score vectors for linear Gaussian state space models.** / Nagakura, Daisuke.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Computing exact score vectors for linear Gaussian state space models

AU - Nagakura, Daisuke

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - 15A99

KW - 60G35

KW - 62H15

KW - Initial condition

KW - Recursive formula

KW - Score test

KW - Score vector

KW - State space model

UR - http://www.scopus.com/inward/record.url?scp=85064738829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064738829&partnerID=8YFLogxK

U2 - 10.1080/03610918.2019.1601216

DO - 10.1080/03610918.2019.1601216

M3 - Article

AN - SCOPUS:85064738829

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

ER -