Bilinear modulation models for seasonal tables of counts

Marx, Brian D.; Eilers, Paul H.C.; Gampe, Jutta; Rau, Roland

doi:10.1007/s11222-009-9144-9

Cited by 6 publications

(3 citation statements)

References 15 publications

(15 reference statements)

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“…A possible approach to capture the seasonal/cyclic patterns in environmental data, and also reduce the computational burden, would be to include specific structures for this setting as, e.g. : smooth components for the trend and the use of periodic (co)sine functions for the seasonal component (see Eilers et al, 2008;Marx et al, 2010), or periodic smoothing with specialized harmonic basis and penalties. However, the use of this type of models when the space-time interaction is present in the data would not avoid the identificability problem addressed in this paper when an ANOVAtype model is considered.…”

Section: Discussionmentioning

confidence: 99%

P-spline ANOVA-type interaction models for spatio-temporal smoothing

Lee

Durbán

2011

Statistical Modelling

113

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In recent years, spatial and spatio-temporal modelling have become an important area of research in many fields (epidemiology, environmental studies, disease mapping, ...). However, most of the models developed are constrained by the large amounts of data available. We propose the use of Penalized splines (P -splines) in a mixed model framework for smoothing spatio-temporal data. Our approach allows the consideration of interaction terms which can be decomposed as a sum of smooth functions similarly as an ANOVA decomposition. The properties of the basis used for regression allow the use of algorithms that can handle large amount of data. We show that imposing the same constraints as in a factorial design it is possible to avoid identifiability problems. We illustrate the methodology for Europe ozone levels in the period 1999-2005.

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Section: Discussionmentioning

confidence: 99%

P-spline ANOVA-type interaction models for spatio-temporal smoothing

Lee

Durbán

2011

Statistical Modelling

113

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“…We have already seen such evidence in this paper by moving from simple to additive P-VCMs, from standard to generalized settings, and from one-dimensional coefficient curves to two-dimensional coefficient surfaces. P-VCMs can also be extended into bilinear models, as presented in Marx et al (2010). In all cases, P-VCMs further remain grounded in classical or generalized (penalized) regression, allowing swift fitting and desirable diagnostics, e.g.…”

Section: Discussion Toward More Complex Vcmsmentioning

confidence: 99%

P-spline Varying Coefficient Models for Complex Data

Marx

2009

Statistical Modelling and Regression Structures

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Although the literature on varying coefficient models (VCMs) is vast, we believe that there remains room to make these models more widely accessible and provide a unified and practical implementation for a variety of complex data settings. The adaptive nature and strength of P-spline VCMs allow a full range of models: from simple to additive structures, from standard to generalized linear models, from onedimensional coefficient curves to two-dimensional (or higher) coefficient surfaces, among others, including bilinear models and signal regression. As P-spline VCMs are grounded in classical or generalized (penalized) regression, fitting is swift and desirable diagnostics are available. We will see that in higher dimensions, tractability is only ensured if efficient array regression approaches are implemented. We also motivate our approaches through several examples, most notably the German deep drill data, to highlight the breadth and utility of our approach.

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“…Our preference is to use summer troughs due to the tendency for sharp peaks in winter and relatively flat troughs in summer (Marx et al, 2010), meaning that winter peaks can be more extreme and variable. From Figure 17(a), the period 2015.5-2019.5 seems to be the most suitable period for estimating the portfolio-specific improvement rate, as the trough in the summer of 2020 may be unusually deep due to brought-forward deaths.…”

Section: Estimating Portfolio-specific Improvementsmentioning

confidence: 99%

Allowing for shocks in portfolio mortality models

Richards¹

2022

Br. Actuar. J.

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The COVID-19 pandemic creates a challenge for actuaries analysing experience data that include mortality shocks. Without sufficient local flexibility in the time dimension, any analysis based on the most recent data will be biased by the temporarily higher mortality. Also, depending on where the shocks sit in the exposure period, any attempt to identify mortality trends will be distorted. We present a methodology for analysing portfolio mortality data that offer local flexibility in the time dimension. The approach permits the identification of seasonal variation, mortality shocks and occurred-but-not reported deaths (OBNR). The methodology also allows actuaries to measure portfolio-specific mortality improvements. Finally, the method assists actuaries in determining a representative mortality level for long-term applications like reserving and pricing, even in the presence of mortality shocks. Results are given for a mature annuity portfolio in the UK, which suggest that the Bayesian information criterion is better for actuarial model selection in this application than Akaike’s information criterion.

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Bilinear modulation models for seasonal tables of counts

Cited by 6 publications

References 15 publications

P-spline ANOVA-type interaction models for spatio-temporal smoothing

P-spline ANOVA-type interaction models for spatio-temporal smoothing

P-spline Varying Coefficient Models for Complex Data

Allowing for shocks in portfolio mortality models

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