Design of watertight subdivision inherently involves its optimization with the objective to increase the index ＂A＂ above its minimum required value. In view of a big popularity of probabilistic search methods such a...Design of watertight subdivision inherently involves its optimization with the objective to increase the index ＂A＂ above its minimum required value. In view of a big popularity of probabilistic search methods such as genetic algorithms, this task is intrinsically time consuming. Thus, even when an optimal subdivision layout （i.e. topology） is determined, it can be found that the optimal bulkhead positions can be a great challenge time-wise, often forcing designers to satisfy with suboptimal solutions. The fundamental reason why this happens is that the nature of the optimized function （e.g., index ＂A＂ as a function of bulkhead positions） is unknown and hence it has no effect upon the choice of optimization strategy, which therefore reflects subjective but not factual preferences. In this paper we study the nature of functional dependency between the subdivision index and bulkhead positions, as a simplest case, and indicate pertinent optimization strategies that consequently reduce the optimization time. In our study we use a cruise ship model to demonstrate the application results of our findings.展开更多
Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for mode...Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data.First,the concepts of Pearson and Kendall correlation coefficients are presented,and the copula theory is briefly introduced.Thereafter,a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula.Second,these two methods are compared in computational efficiency,applicability,and capability of fitting data.Finally,four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method.The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters,but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way.It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data.The Gaussian copula using the Kendall method is superior to that using the Pearson method,which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters.There exists a strong negative correlation between the two parameters underlying load-displacement curves.Neglecting such correlation will not capture the scatter in the measured load-displacement curves.These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.展开更多
This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables....This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.展开更多
When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of ...When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of statistical models could be even more difficult.To this end,this paper proposes a quantile difference method(QDM) that can effectively estimate the heteroscedastic function.This method,being completely free from the estimation of mean regression function,is simple,robust and easy to implement.Moreover,the QDM method enables the detection of heteroscedasticity without any restrictions on error terms,consequently being widely applied.What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained.In the end,the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.展开更多
文摘Design of watertight subdivision inherently involves its optimization with the objective to increase the index ＂A＂ above its minimum required value. In view of a big popularity of probabilistic search methods such as genetic algorithms, this task is intrinsically time consuming. Thus, even when an optimal subdivision layout （i.e. topology） is determined, it can be found that the optimal bulkhead positions can be a great challenge time-wise, often forcing designers to satisfy with suboptimal solutions. The fundamental reason why this happens is that the nature of the optimized function （e.g., index ＂A＂ as a function of bulkhead positions） is unknown and hence it has no effect upon the choice of optimization strategy, which therefore reflects subjective but not factual preferences. In this paper we study the nature of functional dependency between the subdivision index and bulkhead positions, as a simplest case, and indicate pertinent optimization strategies that consequently reduce the optimization time. In our study we use a cruise ship model to demonstrate the application results of our findings.
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2011CB013506)the National Natural Science Foundation of China (Grant Nos. 51028901 and 50839004)
文摘Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data.First,the concepts of Pearson and Kendall correlation coefficients are presented,and the copula theory is briefly introduced.Thereafter,a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula.Second,these two methods are compared in computational efficiency,applicability,and capability of fitting data.Finally,four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method.The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters,but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way.It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data.The Gaussian copula using the Kendall method is superior to that using the Pearson method,which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters.There exists a strong negative correlation between the two parameters underlying load-displacement curves.Neglecting such correlation will not capture the scatter in the measured load-displacement curves.These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.
基金supported by National Natural Science Foundation of China(Grant No.11071120)
文摘This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.
基金supported by the National Natural Science Foundation of China under Grant No.11271368the Major Program of Beijing Philosophy and Social Science Foundation of China under Grant No.15ZDA17+3 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20130004110007the Key Program of National Philosophy and Social Science Foundation under Grant No.13AZD064the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China under Grant No.15XNL008the Project of Flying Apsaras Scholar of Lanzhou University of Finance & Economics
文摘When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of statistical models could be even more difficult.To this end,this paper proposes a quantile difference method(QDM) that can effectively estimate the heteroscedastic function.This method,being completely free from the estimation of mean regression function,is simple,robust and easy to implement.Moreover,the QDM method enables the detection of heteroscedasticity without any restrictions on error terms,consequently being widely applied.What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained.In the end,the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.
