TESTING FOR RANDOM EFFECTS IN COMPOUND RISK MODELS VIA BREGMAN DIVERGENCE
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract The generalized linear model (GLM) is a statistical model which has been widely used in actuarial practices, especially for insurance ratemaking. Due to the inherent longitudinality of property and casualty insurance claim datasets, there have been some trials of incorporating unobserved heterogeneity of each policyholder from the repeated observations. To achieve this goal, random effects models have been proposed, but theoretical discussions of the methods to test the presence of random effects in GLM framework are still scarce. In this article, the concept of Bregman divergence is explored, which has some good properties for statistical modeling and can be connected to diverse model selection diagnostics as in Goh and Dey [(2014) Journal of Multivariate Analysis , 124 , 371–383]. We can apply model diagnostics derived from the Bregman divergence for testing robustness of a chosen prior by the modeler to possible misspecification of prior distribution both on the naive model, which assumes that random effects follow a point mass distribution as its prior distribution, and the proposed model, which assumes a continuous prior density of random effects. This approach provides insurance companies a concrete framework for testing the presence of nonconstant random effects in both claim frequency and severity and furthermore appropriate hierarchical model which can explain both observed and unobserved heterogeneity of the policyholders for insurance ratemaking. Both models are calibrated using a claim dataset from the Wisconsin Local Government Property Insurance Fund which includes both observed claim counts and amounts from a portfolio of policyholders.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.014 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it