该研究建议了主余震型地震动过程的降维模拟方法。首先,在非平稳地震动的演变功率谱密度(evolutionary power spectrum density,EPSD)模型的基础上,提出了演变功率谱密度模型参数的识别方法,并针对实测主余震地震动记录对峰值加速度、...该研究建议了主余震型地震动过程的降维模拟方法。首先,在非平稳地震动的演变功率谱密度(evolutionary power spectrum density,EPSD)模型的基础上,提出了演变功率谱密度模型参数的识别方法,并针对实测主余震地震动记录对峰值加速度、场地土的卓越圆频率和阻尼比以及调制函数参数等模型参数进行了识别;其次,通过拟合优度检验,得到了这些参数的最优边缘分布。然后,利用Copula理论对主余震参数之间的相关结构进行分析,得到了主震参数条件下对应余震参数的条件均值,并通过多项式拟合建立了主余震参数之间的实用计算公式。最后,结合谱表示-随机函数方法,建立了主余震型地震动的降维模型,生成了主余震型地震动的代表性时程。此外,通过与实测主余震记录的反应谱和傅里叶幅值谱的对比分析,验证了该模型的工程适用性。该研究工作以期为主余震型地震动作用下工程结构的随机动力反应分析与可靠度评估提供合理基础。展开更多
This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the...This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the Bayes classification error probability, we propose to use an iterative algorithm to optimize the dimension reduction for classification with a probabilistic approach to achieve the Bayes classifier. The estimated probabilities of different errors encountered along the different phases of the system are realized by the Kernel estimate which is adjusted in a means of the smoothing parameter. Experiment results suggest that the proposed approach performs well.展开更多
Large dimensional predictors are often introduced in regressions to attenuate the possible modeling bias. We consider the stable direction recovery in single-index models in which we solely assume the response Y is in...Large dimensional predictors are often introduced in regressions to attenuate the possible modeling bias. We consider the stable direction recovery in single-index models in which we solely assume the response Y is independent of the diverging dimensional predictors X when βτ 0 X is given, where β 0 is a p n × 1 vector, and p n →∞ as the sample size n →∞. We first explore sufficient conditions under which the least squares estimation β n0 recovers the direction β 0 consistently even when p n = o(√ n). To enhance the model interpretability by excluding irrelevant predictors in regressions, we suggest an e1-regularization algorithm with a quadratic constraint on magnitude of least squares residuals to search for a sparse estimation of β 0 . Not only can the solution β n of e1-regularization recover β 0 consistently, it also produces sufficiently sparse estimators which enable us to select "important" predictors to facilitate the model interpretation while maintaining the prediction accuracy. Further analysis by simulations and an application to the car price data suggest that our proposed estimation procedures have good finite-sample performance and are computationally efficient.展开更多
文摘该研究建议了主余震型地震动过程的降维模拟方法。首先,在非平稳地震动的演变功率谱密度(evolutionary power spectrum density,EPSD)模型的基础上,提出了演变功率谱密度模型参数的识别方法,并针对实测主余震地震动记录对峰值加速度、场地土的卓越圆频率和阻尼比以及调制函数参数等模型参数进行了识别;其次,通过拟合优度检验,得到了这些参数的最优边缘分布。然后,利用Copula理论对主余震参数之间的相关结构进行分析,得到了主震参数条件下对应余震参数的条件均值,并通过多项式拟合建立了主余震参数之间的实用计算公式。最后,结合谱表示-随机函数方法,建立了主余震型地震动的降维模型,生成了主余震型地震动的代表性时程。此外,通过与实测主余震记录的反应谱和傅里叶幅值谱的对比分析,验证了该模型的工程适用性。该研究工作以期为主余震型地震动作用下工程结构的随机动力反应分析与可靠度评估提供合理基础。
文摘This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the Bayes classification error probability, we propose to use an iterative algorithm to optimize the dimension reduction for classification with a probabilistic approach to achieve the Bayes classifier. The estimated probabilities of different errors encountered along the different phases of the system are realized by the Kernel estimate which is adjusted in a means of the smoothing parameter. Experiment results suggest that the proposed approach performs well.
基金supported by National Natural Science Foundation of China (Grant No. 10701035)Chen Guang Project of Shanghai Education Development Foundation (Grant No. 2007CG33)+1 种基金supported by Research Grants Council of Hong KongFaculty Research Grant from Hong Kong Baptist University
文摘Large dimensional predictors are often introduced in regressions to attenuate the possible modeling bias. We consider the stable direction recovery in single-index models in which we solely assume the response Y is independent of the diverging dimensional predictors X when βτ 0 X is given, where β 0 is a p n × 1 vector, and p n →∞ as the sample size n →∞. We first explore sufficient conditions under which the least squares estimation β n0 recovers the direction β 0 consistently even when p n = o(√ n). To enhance the model interpretability by excluding irrelevant predictors in regressions, we suggest an e1-regularization algorithm with a quadratic constraint on magnitude of least squares residuals to search for a sparse estimation of β 0 . Not only can the solution β n of e1-regularization recover β 0 consistently, it also produces sufficiently sparse estimators which enable us to select "important" predictors to facilitate the model interpretation while maintaining the prediction accuracy. Further analysis by simulations and an application to the car price data suggest that our proposed estimation procedures have good finite-sample performance and are computationally efficient.
