Maximization by Parts in Likelihood Inference

Song, Peter X.‐K.; Fan, Yanqin; Kalbfleisch, John D.; Jiang, Jiming; Louis, Thomas A.; Liao, Jiangang; Qaqish, Bahjat F.; Ruppert, David

doi:10.1198/016214505000000204

Cited by 120 publications

(73 citation statements)

References 13 publications

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“…In [46], Czado et al fit Gaussian copula on Poisson frequency and gamma severity and used an optimization by parts method from [53] to do the estimation. They derived the conditional distribution of frequency given severity.…”

Section: Frequency Severity Dependency Modelsmentioning

confidence: 99%

Multivariate Frequency-Severity Regression Models in Insurance

Frees

Lee

Yang

2016

Risks

110

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Abstract:In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one's own vehicle, damage to another party's vehicle, or personal injury. It is also common to be interested in the frequency of accidents in addition to the severity of the claim amounts. This paper synthesizes and extends the literature on multivariate frequency-severity regression modeling with a focus on insurance industry applications. Regression models for understanding the distribution of each outcome continue to be developed yet there now exists a solid body of literature for the marginal outcomes. This paper contributes to this body of literature by focusing on the use of a copula for modeling the dependence among these outcomes; a major advantage of this tool is that it preserves the body of work established for marginal models. We illustrate this approach using data from the Wisconsin Local Government Property Insurance Fund. This fund offers insurance protection for (i) property; (ii) motor vehicle; and (iii) contractors' equipment claims. In addition to several claim types and frequency-severity components, outcomes can be further categorized by time and space, requiring complex dependency modeling. We find significant dependencies for these data; specifically, we find that dependencies among lines are stronger than the dependencies between the frequency and average severity within each line.

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Section: Frequency Severity Dependency Modelsmentioning

confidence: 99%

Multivariate Frequency-Severity Regression Models in Insurance

Frees

Lee

Yang

2016

Risks

110

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“…Maximum likelihood estimation of the parameters in (29) is carried out by maximising the log-likelihood in parts as discussed in Song, Fan and Kalb ‡eisch (2005); see Amado and Teräsvirta (2011) for details. Evaluation of the estimated model is carried out by misspeci…cation tests in Lundbergh and Teräsvirta (2002) that are generalised to this situation.…”

Section: Asymmetric Power Garchmentioning

confidence: 99%

Nonlinear Models for Autoregressive Conditional Heteroskedasticity

Teräsvirta

2012

Handbook of Volatility Models and Their Applications

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“…If we further generalize (3.2) to be a function of µ t as well, we will have θ 2 ) because the density f (C t | t−1 ) will also depend on θ 1 . Since the first part of the likelihood is still a function of θ 1 only, computing the ML estimates can also be done effectively using the method of Song et al (2005). As far as forecasting the covariance is concerned, Category 1 uses more information (both y t and C t ) for modeling C t|t−1 compared to the other two categories.…”

Section: Estimationmentioning

confidence: 99%

Stochastic Covariance Models

2013

JJSS

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A new class of stochastic covariance models based on Wishart distribution is proposed. Three categories of dynamic correlation models are introduced depending on how the time-varying covariance matrix is formulated and whether or not it is a latent variable. A stochastic covariance filter is also developed for filtering and predicting covariances. Extensions of the basic models enable the study of the long memory properties of dynamic correlations, threshold correlation effects and portfolio analysis. Suitable parameterization in the stochastic covariance models and the stochastic covariance filter facilitate efficient calculation of the likelihood function in high-dimensional problems, no matter whether the covariance matrix is observable or latent. Monte Carlo experiments investigating finite sample properties of the maximum likelihood estimator are conducted. Two empirical examples are presented. One deals with the realized covariance of high frequency exchange rate data, while the other examines daily stock returns.

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Maximization by Parts in Likelihood Inference

Cited by 120 publications

References 13 publications

Multivariate Frequency-Severity Regression Models in Insurance

Multivariate Frequency-Severity Regression Models in Insurance

Nonlinear Models for Autoregressive Conditional Heteroskedasticity

Stochastic Covariance Models

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