Liu-Type Regression (LTR) is one of the statistical methods to overcome multicollinearity in multiple regression models. LTR is the development of Ridge regression and Liu estimator. When there is a strong collinearity, selected k parameter in the ridge regression does not fully overcome the multicollinearity. This study aimed to estimate the rainfall data in Pangkep Regency (as response variable) with LTR approach on Statistical Downscaling (SD) models. Precipitation (as predictor variables) is the result of a simulation of a grid on the Global Circulation Model (GCM). This study uses a size 8 8 grid of GCM (64 predictor variables) over an area of Pangkep Regency so that there is a high multicollinearity. Three dummy variables were determined from k-means cluster technique used as predictor variables to overcome the heterogeneity of residual variance. LTR model with dummy variables are able to explain the diversity of rainfall data properly. The value of R2 produced ranges 85.23% -88.99% with Root Mean Square Error (RMSE) ranges 117.732-136.377. Validation of the model generates a high correlation value between the actual rainfall and alleged rainfall period of 2017 (about 0.977-0.979). The value of Root Mean Square Error Prediction (RMSEP) produced lower (about 57.625-61.120). SD analysis was also performed with and without the dummy variable in the Ridge regression and LTR. In general, LRT models with dummy (k = 0.652, d = -0.799) is the best model based on the value of R2, RMSE, correlation, and RMSEP.

The construction of the likelihood equation in the point process models plays a very important role, especially to obtain a good estimator of the parameters of a model. This paper aims to construction of the likelihood of Hawkes process in solving the problem of the claim filing process in the nonlife insurance company. In the construction process, the excitation function with exponential decay is used. The result shows that the total likelihood function of the process depend on probability no claim at time t, the number of policyholder at time t, and the excitation function.