# Variance estimation for integrated population models

Besbeas, Panagiotis, Morgan, Byron J. T. (2017) Variance estimation for integrated population models. Advances in Statistical Analysis, . ISSN 1863-8171. E-ISSN 1863-818X. (doi:10.1007/s10182-017-0304-5) (KAR id:62889)

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http://dx.doi.org/10.1007/s10182-017-0304-5

## Abstract

Abstract State-space models are widely used in ecology. However, it is well known that in practice it can be difficult to estimate both the process and observation variances that occur in such models. We consider this issue for integrated population models,which incorporate state-space models for population dynamics. To some extent, the mechanism of integrated population models protects against this problem, but it can still arise, and two illustrations are provided, in each of which the observation variance is estimated as zero. In the context of an extended case study involving data on British Grey herons, we consider alternative approaches for dealing with the problem when it occurs. In particular, we consider penalised likelihood, a method based on fitting splines and a method of pseudo-replication, which is undertaken via a simple bootstrap procedure. For the case study of the paper, it is shown that when it occurs, an estimate of zero observation variance is unimportant for inference relating to the model parameters of primary interest. This unexpected finding is supported by a simulation study.

Item Type: Article 10.1007/s10182-017-0304-5 Bootstrap; Cross-validation; cubic splines; grey heron; mark-recovery-recapture data; overfitting; penalised likelihood; plug-in method; Process/observation error estimation; state-space models; time-dependent parameters Q Science > QA Mathematics (inc Computing science)Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics Byron Morgan 18 Aug 2017 13:21 UTC 29 May 2019 19:23 UTC https://kar.kent.ac.uk/id/eprint/62889 (The current URI for this page, for reference purposes)