MARSSharveyobsFI {MARSS}

Hessian Matrix via the Harvey (1989) Recursion

Description

Calculates the observed Fisher Information analytically via the recursion by Harvey (1989) as adapted by Holmes (2017) for MARSS models with linear constraints. This is the same as the Hessian of the negative log-likelihood function at the MLEs. This is a utility function in the MARSS-package and is not exported. Use MARSShessian() to access.

Usage

MARSSharveyobsFI(MLEobj)

Arguments

MLEobj

An object of class marssMLE. This object must have a $par element containing MLE parameter estimates from e.g. MARSSkem.

Value

The observed Fisher Information matrix computed via equation 3.4.69 in Harvey (1989). The differentials in the equation are computed in the recursion in equations 3.4.73a to 3.4.74b. See Holmes (2016c) for a discussion of the Harvey (1989) algorithm and Holmes (2017) for the specific implementation of the algorithm for MARSS models with linear constraints.

Harvey (1989) discusses missing observations in section 3.4.7. However, the MARSSharveyobsFI() function implements the approach of Shumway and Stoffer (2006) in section 6.4 for the missing values. See Holmes (2012) for a full discussion of the missing values modifications.

Author(s)

Eli Holmes, NOAA, Seattle, USA.

References

R. H. Shumway and D. S. Stoffer (2006). Section 6.4 (Missing Data Modifications) in Time series analysis and its applications. Springer-Verlag, New York.

Harvey, A. C. (1989) Section 3.4.5 (Information matrix) in Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge, UK.

See also J. E. Cavanaugh and R. H. Shumway (1996) On computing the expected Fisher information matrix for state-space model parameters. Statistics & Probability Letters 26: 347-355. This paper discusses the Harvey (1989) recursion (and proposes an alternative).

Holmes, E. E. (2012). Derivation of the EM algorithm for constrained and unconstrained multivariate autoregressive state-space (MARSS) models. Technical Report. arXiv:1302.3919 [stat.ME]

Holmes, E. E. 2016c. Notes on computing the Fisher Information matrix for MARSS models. Part III Overview of Harvey 1989. https://eeholmes.github.io/posts/2016-6-16-FI-recursion-3/

Holmes, E. E. 2017. Notes on computing the Fisher Information matrix for MARSS models. Part IV Implementing the Recursion in Harvey 1989. https://eeholmes.github.io/posts/2017-5-31-FI-recursion-4/

See Also

MARSShessian(), MARSSparamCIs()

Examples

dat <- t(harborSeal)
dat <- dat[c(2, 11), ]
fit <- MARSS(dat)
MARSS:::MARSSharveyobsFI(fit)