Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the...Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.展开更多
In order to reduce the uncertainty of offline land surface model （LSM） simulations of land evapotranspiration （ET）, we used ensemble simulations based on three meteorological forcing datasets [Princeton, ITPCAS （...In order to reduce the uncertainty of offline land surface model （LSM） simulations of land evapotranspiration （ET）, we used ensemble simulations based on three meteorological forcing datasets [Princeton, ITPCAS （Institute of Tibetan Plateau Research, Chinese Academy of Sciences）, Qian] and four LSMs （BATS, VIC, CLM3.0 and CLM3.5）, to explore the trends and spatiotemporal characteristics of ET, as well as the spatiotemporal pattern of ET in response to climate factors over China's Mainland during 1982-2007. The results showed that various simulations of each member and their arithmetic mean （EnsAVlean） could capture the spatial distribution and seasonal pattern of ET sufficiently well, where they exhibited more significant spatial and seasonal variation in the ET compared with observation-based ET estimates （Obs_MTE）. For the mean annual ET, we found that the BATS forced by Princeton forcing overestimated the annual mean ET compared with Obs_MTE for most of the basins in China, whereas the VIC forced by Princeton forcing showed underestimations. By contrast, the Ens_Mean was closer to Obs_MTE, although the results were underestimated over Southeast China. Furthermore, both the Obs_MTE and Ens_Mean exhibited a significant increasing trend during 1982-98; whereas after 1998, when the last big EI Nifio event occurred, the Ens_Mean tended to decrease significantly between 1999 and 2007, although the change was not significant for Obs_MTE. Changes in air temperature and shortwave radiation played key roles in the long-term variation in ET over the humid area of China, but precipitation mainly controlled the long-term variation in ET in arid and semi-arid areas of China.展开更多
In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average varianc...In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.展开更多
In this paper, H∞ optimal model reduction for singular fast subsystems will be inves-tigated. First, error system is established to measure the error magnitude between the original andreduced systems, and it is demon...In this paper, H∞ optimal model reduction for singular fast subsystems will be inves-tigated. First, error system is established to measure the error magnitude between the original andreduced systems, and it is demonstrated that the new feature for model reduction of singular systemsis to make H∞ norm of the error system finite and minimal. The necessary and su?cient conditionis derived for the existence of the H∞ suboptimal model reduction problem. Next, we give an exactand practicable algorithm to get the parameters of the reduced subsystems by applying the matrixtheory. Meanwhile, the reduced system may be also impulsive. The advantages of the proposedalgorithm are that it is more ?exible in a straight-forward way without much extra computation, andthe order of the reduced systems is as minimal as possible. Finally, one illustrative example is givento illustrate the e?ectiveness of the proposed model reduction approach.展开更多
文摘Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.4140508391437220 and 41305066)+1 种基金the Natural Science Foundation of Hunan Province(Grant No.2015JJ3098)the Fund Project for The Education Department of Hunan Province(Grant No.14C0897)
文摘In order to reduce the uncertainty of offline land surface model （LSM） simulations of land evapotranspiration （ET）, we used ensemble simulations based on three meteorological forcing datasets [Princeton, ITPCAS （Institute of Tibetan Plateau Research, Chinese Academy of Sciences）, Qian] and four LSMs （BATS, VIC, CLM3.0 and CLM3.5）, to explore the trends and spatiotemporal characteristics of ET, as well as the spatiotemporal pattern of ET in response to climate factors over China's Mainland during 1982-2007. The results showed that various simulations of each member and their arithmetic mean （EnsAVlean） could capture the spatial distribution and seasonal pattern of ET sufficiently well, where they exhibited more significant spatial and seasonal variation in the ET compared with observation-based ET estimates （Obs_MTE）. For the mean annual ET, we found that the BATS forced by Princeton forcing overestimated the annual mean ET compared with Obs_MTE for most of the basins in China, whereas the VIC forced by Princeton forcing showed underestimations. By contrast, the Ens_Mean was closer to Obs_MTE, although the results were underestimated over Southeast China. Furthermore, both the Obs_MTE and Ens_Mean exhibited a significant increasing trend during 1982-98; whereas after 1998, when the last big EI Nifio event occurred, the Ens_Mean tended to decrease significantly between 1999 and 2007, although the change was not significant for Obs_MTE. Changes in air temperature and shortwave radiation played key roles in the long-term variation in ET over the humid area of China, but precipitation mainly controlled the long-term variation in ET in arid and semi-arid areas of China.
文摘In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.
文摘In this paper, H∞ optimal model reduction for singular fast subsystems will be inves-tigated. First, error system is established to measure the error magnitude between the original andreduced systems, and it is demonstrated that the new feature for model reduction of singular systemsis to make H∞ norm of the error system finite and minimal. The necessary and su?cient conditionis derived for the existence of the H∞ suboptimal model reduction problem. Next, we give an exactand practicable algorithm to get the parameters of the reduced subsystems by applying the matrixtheory. Meanwhile, the reduced system may be also impulsive. The advantages of the proposedalgorithm are that it is more ?exible in a straight-forward way without much extra computation, andthe order of the reduced systems is as minimal as possible. Finally, one illustrative example is givento illustrate the e?ectiveness of the proposed model reduction approach.
