A Mixture Model for Payments and Payment Numbers in Claims Reserving

Gigante, Patrizia; Picech, Liviana; Sigalotti, L.

doi:10.1017/asb.2016.30

Cited by 4 publications

(4 citation statements)

References 38 publications

(55 reference statements)

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“…Because the likelihood function does not have a closed form, either a numerical approximation such as the Gauss‐Hermite quadrature 24 or an EM algorithm may be used to estimate the parameters of interest, that is,

\left({\gamma}_0,{\gamma}_1,{\beta}_0,{\beta}_1,{\delta}_0,{\delta}_1,\Sigma \right)

. Gigante 25 developed a numerical estimating procedure for the joint mixed effects model on the number of health insurance payments and the increment payments, in the context of the sleep model, on

\left(M,Y\right)

. Specifically, they used a hierarchical likelihood approach 26 and an iterative weighted least square algorithm.…”

Section: Models and Methodsmentioning

confidence: 99%

Jointly modeling of sleep variables that are objectively measured by wrist actigraphy

Xue

Hua

Weber

et al. 2022

Statistics in Medicine

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Recently developed actigraphy devices have made it possible for continuous and objective monitoring of sleep over multiple nights. Sleep variables captured by wrist actigraphy devices include sleep onset, sleep end, total sleep time, wake time after sleep onset, number of awakenings, etc. Currently available statisticalmethods to analyze such actigraphy data have limitations. First, averages over multiple nights are used to summarize sleep activities, ignoring variability over multiple nights from the same subject. Second, sleep variables are often analyzed independently. However, sleep variables tend to be correlated with each other. For example, how long a subject sleeps at night can be correlated with how long and how frequent he/she wakes up during that night. It is important to understand these inter-relationships. We therefore propose a joint mixed effect model on total sleep time, number of awakenings, and wake time. We develop an estimating procedure based upon a sequence of generalized linear mixed effects models, which can be implemented using existing software. The use of these models not only avoids computational intensity and instability that may occur by directly applying a numerical algorithm on a complicated joint likelihood function, but also provides additional insights on sleep activities. We demonstrated in simulation studies that the proposed estimating procedure performed well in estimating both fixed and random effects' parameters. We applied the proposed model to data from the Women's Interagency HIV Sleep Study to examine the association of employment status and age with overall sleep quality assessed by several actigraphy measured sleep variables.

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\left({\gamma}_0,{\gamma}_1,{\beta}_0,{\beta}_1,{\delta}_0,{\delta}_1,\Sigma \right)

. Gigante 25 developed a numerical estimating procedure for the joint mixed effects model on the number of health insurance payments and the increment payments, in the context of the sleep model, on

\left(M,Y\right)

. Specifically, they used a hierarchical likelihood approach 26 and an iterative weighted least square algorithm.…”

Section: Models and Methodsmentioning

confidence: 99%

Jointly modeling of sleep variables that are objectively measured by wrist actigraphy

Xue

Hua

Weber

et al. 2022

Statistics in Medicine

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show abstract

“…We do not explain here in detail the estimation approach, since it can be obtained by simple adaption of the procedures described in Gigante et al (2013aGigante et al ( , 2016. We just outline it and remark some specific aspects of the current model.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…As a measure of prediction uncertainty, we use the conditional MSEP which takes account of the fluctuations of the outstanding claims around the pre-dictorR. As in previous papers on claims reserve evaluation in the HGLM approach (see Gigante et al, 2013aGigante et al, , 2013bGigante et al, , 2016, we use an approximate formula for the MSEP based on the following decomposition:…”

Section: Reserve Prediction and Prediction Errormentioning

confidence: 99%

Calendar Year Effect Modeling for Claims Reserving in HGLM

Gigante¹,

Picech²,

Sigalotti³

2019

ASTIN Bull.

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Claims reserving models are usually based on data recorded in run-off tables, according to the origin and the development years of the payments. The amounts on the same diagonal are paid in the same calendar year and are influenced by some common effects, for example, claims inflation, that can induce dependence among payments. We introduce hierarchical generalized linear models (HGLM) with risk parameters related to the origin and the calendar years, in order to model the dependence among payments of both the same origin year and the same calendar year. Besides the random effects, the linear predictor also includes fixed effects. All the parameters are estimated within the model by the h-likelihood approach. The prediction for the outstanding claims and an approximate formula to evaluate the mean square error of prediction are obtained. Moreover, a parametric bootstrap procedure is delineated to get an estimate of the predictive distribution of the outstanding claims. A Poisson-gamma HGLM with origin and calendar year effects is studied extensively and a numerical example is provided. We find that the estimates of the correlations can be significant for payments in the same calendar year and that the inclusion of calendar effects can determine a remarkable impact on the prediction uncertainty.

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“…The power parameter was estimated by a trial-and-error method. Gigante et al (2013Gigante et al ( , 2016 also assumed the dispersion parameter as a regression function. Gigante et al (2016) proposed a mixture model framework, and applied the hierarchical loglikelihood method (Lee and Nelder, 2001) to estimate parameters via three iterative GLMs.…”

Section: Introductionmentioning

confidence: 99%

Compound Poisson Claims Reserving Models: Extensions and Inference

Meng

Gao

2018

ASTIN Bull.

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We consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.

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A Mixture Model for Payments and Payment Numbers in Claims Reserving

Cited by 4 publications

References 38 publications

Jointly modeling of sleep variables that are objectively measured by wrist actigraphy

Jointly modeling of sleep variables that are objectively measured by wrist actigraphy

Calendar Year Effect Modeling for Claims Reserving in HGLM

Compound Poisson Claims Reserving Models: Extensions and Inference

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