[논문]상대오차예측을 이용한 자동차 보험의 손해액 예측: 패널자료를 이용한 연구

박흥선

doi:10.5351/kjas.2021.34.5.697

상대오차예측을 이용한 자동차 보험의 손해액 예측: 패널자료를 이용한 연구
Predicting claim size in the auto insurance with relative error: a panel data approach 원문보기

응용통계연구 = The Korean journal of applied statistics, v.34 no.5, 2021년, pp.697 - 710

초록
AI-Helper

상대오차를 이용한 예측법은 상대오차(혹은 퍼센트오차)가 중요시되는 분야, 특히 계량경제학이나 소프트웨어 엔지니어링, 또는 정부기관 공식통계 부분에서 기존 예측방법 외에 선호되는 예측방법이다. 그 동안 상대오차를 이용한 예측법은 선형 혹은 비선형 회귀분석 뿐 아니라, 커널회귀를 이용한 비모수 회귀모형, 그리고 정상시계열분석에 이르기까지 그 범위가 확장되어 왔다. 그러나, 지금까지의 분석은 고정효과(fixed effect)만을 고려한 것이어서 임의효과(random effect)에 관한 상대오차 예측법에 대한 확장이 필요하였다. 본 논문의 목적은 상대오차예측법을 일반화선형혼합모형(GLMM)에 속한 감마회귀(gamma regression), 로그정규회귀(lognormal regression), 그리고 역가우스회귀(inverse gaussian regression)의 패널자료(panel data)에 적용시키는데 있다. 이를 위해 실제 자동차 보험회사의 손해액 자료를 사용하였고, 최량예측량과 최량상대오차예측량을 각각 적용-비교해 보았다.

Abstract ▼ AI-Helper

Relative error prediction is preferred over ordinary prediction methods when relative/percentile errors are regarded as important, especially in econometrics, software engineering and government official statistics. The relative error prediction techniques have been developed in linear/nonlinear regression, nonparametric regression using kernel regression smoother, and stationary time series models. However, random effect models have not been used in relative error prediction. The purpose of this article is to extend relative error prediction to some of generalized linear mixed model (GLMM) with panel data, which is the random effect models based on gamma, lognormal, or inverse gaussian distribution. For better understanding, the real auto insurance data is used to predict the claim size, and the best predictor and the best relative error predictor are comparatively illustrated.

주제어

표/그림 (7)

그림 Figure 1: Goodness of fit for the inverse gaussian distribution on the claim size, claimcst0.
표 Table 1: The list of variables used from datacar
표 Table 2: The summary of goodness of fit using proc severity for the claim size, claimcst0, and the column-wise optimals (* )
$Table 3: The prediction of the random effect, area (<TEX>$\hat{{\gamma}}_i$</TEX>) using proc glimmix$ 표 Table 3: The prediction of the random effect, area ($\hat{{\gamma}}_i$) using proc glimmix
그림 Figure 2: The predicted claim sizes (claimcst0) with respect to area (area) and driver age (agecat): best predictor (BP: o) and best relative error predictor (BREP: x).
그림 Figure 3: The predicted claim sizes (claimcst0) with respect to area (area) and vehicle age (veh age): best predictor (BP: o) and best relative error predictor (BREP: x).
그림 Figure 4: The predicted claim sizes (claimcst0) with respect to area (area) and gender (gender): best predictor (BP: o) and best relative error predictor (BREP: x).

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