Journal of Applied & Computational Mathematics

A Spatial-Nonparametric Approach for Prediction of Claim Frequency in Motor Car Insurance

Abstract

Kipngetich Gideon*

Spatial modeling has largely been applied in epidemiology and disease modeling. Different methods such as generalized linear models (GLMs), Poisson regression models, and Bayesian Models have been made available to predict the claim frequency for forthcoming years. However, due to the heterogeneous nature of policies, these methods do not produce precise and reliable prediction of future claim frequencies; these traditional statistical methods rely heavily on limiting assumptions including linearity, normality, predictor variable independence, and an established functional structure connecting the criterion and predictive variables. This study investigated how to construct a spatial nonparametric regression model estimator tor for prediction of claim frequency of insurance claims data. The study adopted a nonparametric function based on smoothing Spline in constructing the model. The asymptotic properties of the estimators; normality and consistency were derived and the inferences on the smooth function were derived. The simulation study showed that the estimator that incorporated spatial effects in predicting claims frequency is more efficient than the traditional Simultaneous Autoregressive model and Nonparametric model with Simultaneous Autoregressive error. The model estimator was applied to claims data from Cooperative Insurance Company insurance in Kenya with n = 6500 observations and the findings showed that the proposed model estimator is more efficient compared to the Local Linear fitted method, which does not account for spatial correlation. Therefore, the proposed method (Nonparametric spatial estimator) based on the findings has significant statistical improvement of the existing methods that are used for the prediction of claims. The study had a number of limitations, where the data used in the study is Lattice data (without a coordinate system); therefore, there was difficulty in classifying the claims to a specific area in the region (County).