The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parame...The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.展开更多
Sensitivity analysis(SA) has been widely used to screen out a small number of sensitive parameters for model outputs from all adjustable parameters in weather and climate models, helping to improve model predictions b...Sensitivity analysis(SA) has been widely used to screen out a small number of sensitive parameters for model outputs from all adjustable parameters in weather and climate models, helping to improve model predictions by tuning the parameters. However, most parametric SA studies have focused on a single SA method and a single model output evaluation function, which makes the screened sensitive parameters less comprehensive. In addition, qualitative SA methods are often used because simulations using complex weather and climate models are time-consuming. Unlike previous SA studies, this research has systematically evaluated the sensitivity of parameters that affect precipitation and temperature simulations in the Weather Research and Forecasting(WRF) model using both qualitative and quantitative global SA methods. In the SA studies, multiple model output evaluation functions were used to conduct various SA experiments for precipitation and temperature. The results showed that five parameters(P3, P5, P7, P10, and P16) had the greatest effect on precipitation simulation results and that two parameters(P7 and P10) had the greatest effect for temperature. Using quantitative SA, the two-way interactive effect between P7 and P10 was also found to be important, especially for precipitation. The microphysics scheme had more sensitive parameters for precipitation, and P10(the multiplier for saturated soil water content) was the most sensitive parameter for both precipitation and temperature. From the ensemble simulations, preliminary results indicated that the precipitation and temperature simulation accuracies could be improved by tuning the respective sensitive parameter values, especially for simulations of moderate and heavy rain.展开更多
From the insurer＇s point of view, this paper studies the optimal investment and proportional reinsurance in the Sparre Andersen model. Under the criterion of maximizing the adjustment coefficient, the authors obtain ...From the insurer＇s point of view, this paper studies the optimal investment and proportional reinsurance in the Sparre Andersen model. Under the criterion of maximizing the adjustment coefficient, the authors obtain the closed form expressions of the optimal strategy and the maximal adjustment coefficient, and derive the explicit expression of the ruin probability or its lower bound when the claim sizes are exponentially distributed. Some numerical examples are presented, which show the impact of model parameters on the optimal values. It can also be seen that the optimal strategy to maximize the adjustment coefficient is sometimes equivalent to those which minimize the ruin probability.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.10771017 and 11071022Key Project of MOE,PRC under Grant No.309007
文摘The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin （1976） is considered in this paper. A constrained empirical likelihood confidence region for a parameter β0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation＇s conclusion.
基金supported by the Special Fund for Meteorological Scientific Research in the Public Interest (Grant No. GYHY201506002, CRA40: 40-year CMA global atmospheric reanalysis)the National Basic Research Program of China (Grant No. 2015CB953703)+1 种基金the Intergovernmental Key International S & T Innovation Cooperation Program (Grant No. 2016YFE0102400)the National Natural Science Foundation of China (Grant Nos. 41305052 & 41375139)
文摘Sensitivity analysis(SA) has been widely used to screen out a small number of sensitive parameters for model outputs from all adjustable parameters in weather and climate models, helping to improve model predictions by tuning the parameters. However, most parametric SA studies have focused on a single SA method and a single model output evaluation function, which makes the screened sensitive parameters less comprehensive. In addition, qualitative SA methods are often used because simulations using complex weather and climate models are time-consuming. Unlike previous SA studies, this research has systematically evaluated the sensitivity of parameters that affect precipitation and temperature simulations in the Weather Research and Forecasting(WRF) model using both qualitative and quantitative global SA methods. In the SA studies, multiple model output evaluation functions were used to conduct various SA experiments for precipitation and temperature. The results showed that five parameters(P3, P5, P7, P10, and P16) had the greatest effect on precipitation simulation results and that two parameters(P7 and P10) had the greatest effect for temperature. Using quantitative SA, the two-way interactive effect between P7 and P10 was also found to be important, especially for precipitation. The microphysics scheme had more sensitive parameters for precipitation, and P10(the multiplier for saturated soil water content) was the most sensitive parameter for both precipitation and temperature. From the ensemble simulations, preliminary results indicated that the precipitation and temperature simulation accuracies could be improved by tuning the respective sensitive parameter values, especially for simulations of moderate and heavy rain.
基金supported by the National Natural Science Foundation of China under Grant No.11101215the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 09KJB110004
文摘From the insurer＇s point of view, this paper studies the optimal investment and proportional reinsurance in the Sparre Andersen model. Under the criterion of maximizing the adjustment coefficient, the authors obtain the closed form expressions of the optimal strategy and the maximal adjustment coefficient, and derive the explicit expression of the ruin probability or its lower bound when the claim sizes are exponentially distributed. Some numerical examples are presented, which show the impact of model parameters on the optimal values. It can also be seen that the optimal strategy to maximize the adjustment coefficient is sometimes equivalent to those which minimize the ruin probability.
