Since the non-unique solution exists in the inversion for finite-fault rupture history, the random weighting method hasbeen used to estimate error of the inversion results in this paper. The resolution distributions o...Since the non-unique solution exists in the inversion for finite-fault rupture history, the random weighting method hasbeen used to estimate error of the inversion results in this paper. The resolution distributions of slip amplitude, rake,rupture time and rise time on the finite fault were deduced quantitatively by model calculation. By using the randomweighting method, the inversion results of Taiwan Strait earthquake and Myanmar-China boundal earthquake showthat the parameters related to the rupture centers of two events have the highest resolution, and the solutinn are the mostreliable(otherwise the resolution of the slip amplitudes and rise time on the finite-fault boundary is low.展开更多
A new threshold secret sharing scheme is constructed by introducing the concept of share vector, in which the number of shareholders can be adjusted by randomly changing the weights of them. This kind of scheme overco...A new threshold secret sharing scheme is constructed by introducing the concept of share vector, in which the number of shareholders can be adjusted by randomly changing the weights of them. This kind of scheme overcomes the limitation of the static weighted secret sharing schemes that cannot change the weights in the process of carrying out and the deficiency of low efficiency of the ordinary dynamic weighted sharing schemes for its resending process. Thus, this scheme is more suitable to the case that the number of shareholders needs to be changed randomly during the scheme is carrying out.展开更多
In this paper,Edgeworth expansion for the nearest neighbor\|kernel estimate and random weighting approximation of conditional density are given and the consistency and convergence rate are proved.
A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being l...A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap method.It turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with or without an intercept term.The simulation results show that the statistic has a desired finite sample performance in terms of both size and power.A real data application is also given relying on the inflation rate data of 17 countries.展开更多
This paper presents a new random weighting estimation method for dynamic navigation positioning. This method adopts the concept of random weighting estimation to estimate the covariance matrices of system state noises...This paper presents a new random weighting estimation method for dynamic navigation positioning. This method adopts the concept of random weighting estimation to estimate the covariance matrices of system state noises and observation noises for controlling the disturbances of singular observations and the kinematic model errors. It satisfies the practical requirements of the residual vector and innovation vector to sufficiently utilize observation information, thus weakening the disturbing effect of the kinematic model error and observation model error on the state parameter estimation. Theories and algorithms of random weighting estimation are established for estimating the covariance matrices of observation residual vectors and innovation vec- tors. This random weighting estimation method provides an effective solution for improving the positioning accuracy in dynamic navigation. Experimental results show that compared with the Kalman filtering, the extended Kalman filtering and the adaptive windowing filtering, the proposed method can adaptively determine the covariance matrices of observation error and state error, effectively resist the disturbances caused by system error and observation error, and significantly improve the positioning accu- racy for dynamic navigation.展开更多
Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model.In this paper we extend the result to the censored regression model (or censored “...Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model.In this paper we extend the result to the censored regression model (or censored “Tobit” model).展开更多
Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival d...Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap method is and can produce good variance estimates or confidence intervals.展开更多
In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the ran...In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.展开更多
The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution a...The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic. It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.展开更多
In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong ...In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.展开更多
In this paper, a strongly consistent estimation of the optimal trimming proportion in trimmed mean is found by the random weighting method. In addition, using the same method a strongly consistent estimation for the d...In this paper, a strongly consistent estimation of the optimal trimming proportion in trimmed mean is found by the random weighting method. In addition, using the same method a strongly consistent estimation for the distribution of some adaptive estimator is also obtained.展开更多
The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likeli...The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox model.This method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap approximation.In this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed method.Monte Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.展开更多
According to the Projection Pursuit (PP) method and the random weighting method, we propose a PP random weighting method, and set up the asymptotic distribution theory and strong limit theorem of PP random weighting e...According to the Projection Pursuit (PP) method and the random weighting method, we propose a PP random weighting method, and set up the asymptotic distribution theory and strong limit theorem of PP random weighting empirical process. Applying this method, we obtain two kinds of goodness-of-fit test for a multivariate distribution function, i. e., we get the random weighting approximations of PP Kolmogorov Smirnov statistics (PPKS) and PP Smirnov Cramer Von Mises statistics (PPSC), we prove that the asymptotic distribution of PPKS and PPSC are the same as those of their respective random weighting approximations.展开更多
In this paper, we give an one-term Edgeworth expansion for the standardized least square estimator (LSE) in a linear regression model and its random weighting approximation. So we have not only improved the expansion ...In this paper, we give an one-term Edgeworth expansion for the standardized least square estimator (LSE) in a linear regression model and its random weighting approximation. So we have not only improved the expansion result but also given a practical approximating method.展开更多
For the dislribulion if mean error under independent but not identicallydislribuled conditions. its approximating dislribution whose precision reachO is obtained.
The random weighting method is an emerging computing method in statistics.In this paper,we propose a novel estimation of the survival function for right censored data based on the random weighting method.Under some re...The random weighting method is an emerging computing method in statistics.In this paper,we propose a novel estimation of the survival function for right censored data based on the random weighting method.Under some regularity conditions,we prove the strong consistency of this estimation.展开更多
In this paper, we have constructed a random weighting statistic to approximate the distribution of studentized least square estimator in a linear regression model with ideal accuracy o(n<sup>-1/2</sup>). T...In this paper, we have constructed a random weighting statistic to approximate the distribution of studentized least square estimator in a linear regression model with ideal accuracy o(n<sup>-1/2</sup>). Thus, we have provided a more practical distribution approximating method.展开更多
Based on conventional particle swarm optimization(PSO),this paper presents an efficient and reliable heuristic approach using PSO with an adaptive random inertia weight(ARIW)strategy,referred to as the ARIW-PSO algori...Based on conventional particle swarm optimization(PSO),this paper presents an efficient and reliable heuristic approach using PSO with an adaptive random inertia weight(ARIW)strategy,referred to as the ARIW-PSO algorithm,to build a multi-objective optimization model for reservoir operation.Using the triangular probability density function,the inertia weight is randomly generated,and the probability density function is automatically adjusted to make the inertia weight generally greater in the initial stage of evolution,which is suitable for global searches.In the evolution process,the inertia weight gradually decreases,which is beneficial to local searches.The performance of the ARIWPSO algorithm was investigated with some classical test functions,and the results were compared with those of the genetic algorithm(GA),the conventional PSO,and other improved PSO methods.Then,the ARIW-PSO algorithm was applied to multi-objective optimal dispatch of the Panjiakou Reservoir and multi-objective flood control operation of a reservoir group on the Luanhe River in China,including the Panjiakou Reservoir,Daheiting Reservoir,and Taolinkou Reservoir.The validity of the multi-objective optimization model for multi-reservoir systems based on the ARIW-PSO algorithm was verified.展开更多
In this note, the random weighting approximations for empirical process indexed by abounded class of functions are obtained, and the strong uniform convergence rates of ran-dom weighting empirical processes are given....In this note, the random weighting approximations for empirical process indexed by abounded class of functions are obtained, and the strong uniform convergence rates of ran-dom weighting empirical processes are given. When unknown multivariate underlingdistributions are not confined by any additional condition, we obtain the random weightingapproximations for multivariate Von Mises statistics and their projection pursuits (PP). Thisresult is also true for the bootstrap approximation of empirical processes.展开更多
文摘Since the non-unique solution exists in the inversion for finite-fault rupture history, the random weighting method hasbeen used to estimate error of the inversion results in this paper. The resolution distributions of slip amplitude, rake,rupture time and rise time on the finite fault were deduced quantitatively by model calculation. By using the randomweighting method, the inversion results of Taiwan Strait earthquake and Myanmar-China boundal earthquake showthat the parameters related to the rupture centers of two events have the highest resolution, and the solutinn are the mostreliable(otherwise the resolution of the slip amplitudes and rise time on the finite-fault boundary is low.
基金supported by the National Preeminent Youth Foundation(70225002)the Doctor Foundation of North China Electric Power University(200822029).
文摘A new threshold secret sharing scheme is constructed by introducing the concept of share vector, in which the number of shareholders can be adjusted by randomly changing the weights of them. This kind of scheme overcomes the limitation of the static weighted secret sharing schemes that cannot change the weights in the process of carrying out and the deficiency of low efficiency of the ordinary dynamic weighted sharing schemes for its resending process. Thus, this scheme is more suitable to the case that the number of shareholders needs to be changed randomly during the scheme is carrying out.
文摘In this paper,Edgeworth expansion for the nearest neighbor\|kernel estimate and random weighting approximation of conditional density are given and the consistency and convergence rate are proved.
基金supported by the NNSF of China(Grant Nos.11971208 and 11601197)the NNSF of China(Grant No.61973145)+5 种基金the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province(Grant No.20224ACB211003)supported by the Science and Technology Research Project of Education Department of Jiangxi Province(Grant No.GJJ200545)the Postgraduate Innovation Project of Jiangxi Province(Grant No.YC2021–B124)NSSF of China(Grant No.21BTJ035)supported by the National Major Social Science Project of China(Grant No.21&ZD152)Natural Science Project of Jiangxi Provincial Department of Science and Technology(Grant No.jxsq2023201048)。
文摘A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root test.In this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap method.It turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with or without an intercept term.The simulation results show that the statistic has a desired finite sample performance in terms of both size and power.A real data application is also given relying on the inflation rate data of 17 countries.
基金National Natural Science Foundation of China(60574034)Aeronautical Science Foundation of China(20080818004)
文摘This paper presents a new random weighting estimation method for dynamic navigation positioning. This method adopts the concept of random weighting estimation to estimate the covariance matrices of system state noises and observation noises for controlling the disturbances of singular observations and the kinematic model errors. It satisfies the practical requirements of the residual vector and innovation vector to sufficiently utilize observation information, thus weakening the disturbing effect of the kinematic model error and observation model error on the state parameter estimation. Theories and algorithms of random weighting estimation are established for estimating the covariance matrices of observation residual vectors and innovation vec- tors. This random weighting estimation method provides an effective solution for improving the positioning accuracy in dynamic navigation. Experimental results show that compared with the Kalman filtering, the extended Kalman filtering and the adaptive windowing filtering, the proposed method can adaptively determine the covariance matrices of observation error and state error, effectively resist the disturbances caused by system error and observation error, and significantly improve the positioning accu- racy for dynamic navigation.
基金This research is partially supported by National Natural Science Foundation of China(Grant No. 10171094) Ph. D. Program Foundation of the Ministry of Education of China Special Foundations of the Chinese Academy of Sciences and USTC.
文摘Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model.In this paper we extend the result to the censored regression model (or censored “Tobit” model).
基金the National Natural Science Foundation of China (Grant Nos. 10471136, 10671189)PhD Program Foundation of Ministry of Education of China and Foundations from the Chinese Academy of Sciences
文摘Variance of parameter estimate in Cox’s proportional hazards model is based on asymptotic variance. When sample size is small, variance can be estimated by bootstrap method. However, if censoring rate in a survival data set is high, bootstrap method may fail to work properly. This is because bootstrap samples may be even more heavily censored due to repeated sampling of the censored observations. This paper proposes a random weighting method for variance estimation and confidence interval estimation for proportional hazards model. This method, unlike the bootstrap method, does not lead to more severe censoring than the original sample does. Its large sample properties are studied and the consistency and asymptotic normality are proved under mild conditions. Simulation studies show that the random weighting method is not as sensitive to heavy censoring as bootstrap method is and can produce good variance estimates or confidence intervals.
基金supported by a grant from Ferdowsi University of Mashhad(NO.2/42843)
文摘In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.
基金This work was partially supported by the National Natural Science Foundation of China (Grant No. 10471136) Ph. D. Program Foundation of the Ministry of Education of China, Special Foundations of the Chinese Academy of Sciences and USTCIMS Program-Semi-parametric Methods for Survival and Longitudinal Data in National University of Singapore.
文摘The M-test has been in common use and widely studied in testing the linear hypotheses in linear models. However, the critical value for the test is usually related to the quantities of the unknown error distribution and the estimate of the nuisance parameters may be rather involved, not only for the M-test method but also for the existing bootstrap methods. In this paper we suggest a random weighting resampling method for approximating the null distribution of the M-test statistic. It is shown that, under both the null and the local alternatives, the random weighting statistic has the same asymptotic distribution as the null distribution of the M-test. The critical values of the M-test can therefore be obtained by the random weighting method without estimating the nuisance parameters. A distinguished feature of the proposed method is that the approximation is valid even the null hypothesis is not true and the power evaluation is possible under the local alternatives.
基金Supported by the Natural Science Foundation of Beijing City of China (1042002)the Science and Technology Development Foundation of Education Committee of Beijing Citythe Special Expenditure of Excellent Person Education of Beijing(20041D0501515)
文摘In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.
基金Supported by the NNSF of Chinathe Doctoral Foundation of the Institutions Higher Learning of China
文摘In this paper, a strongly consistent estimation of the optimal trimming proportion in trimmed mean is found by the random weighting method. In addition, using the same method a strongly consistent estimation for the distribution of some adaptive estimator is also obtained.
基金supported by Natural Science and Engineering Research Council of Canada and National Natural Science Foundation of China (Grant No. 10871188)
文摘The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox model.This method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap approximation.In this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed method.Monte Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.
基金Supported by the National Natural Science Foundation of China
文摘According to the Projection Pursuit (PP) method and the random weighting method, we propose a PP random weighting method, and set up the asymptotic distribution theory and strong limit theorem of PP random weighting empirical process. Applying this method, we obtain two kinds of goodness-of-fit test for a multivariate distribution function, i. e., we get the random weighting approximations of PP Kolmogorov Smirnov statistics (PPKS) and PP Smirnov Cramer Von Mises statistics (PPSC), we prove that the asymptotic distribution of PPKS and PPSC are the same as those of their respective random weighting approximations.
文摘In this paper, we give an one-term Edgeworth expansion for the standardized least square estimator (LSE) in a linear regression model and its random weighting approximation. So we have not only improved the expansion result but also given a practical approximating method.
文摘For the dislribulion if mean error under independent but not identicallydislribuled conditions. its approximating dislribution whose precision reachO is obtained.
文摘The random weighting method is an emerging computing method in statistics.In this paper,we propose a novel estimation of the survival function for right censored data based on the random weighting method.Under some regularity conditions,we prove the strong consistency of this estimation.
基金Supported by the Doctoral Program Foundation of the Institute of Higher Educationthe National Natural Science Foundation of China.
文摘In this paper, we have constructed a random weighting statistic to approximate the distribution of studentized least square estimator in a linear regression model with ideal accuracy o(n<sup>-1/2</sup>). Thus, we have provided a more practical distribution approximating method.
基金supported by the Foundation of the Scientific and Technological Innovation Team of Colleges and Universities in Henan Province(Grant No.181RTSTHN009)the Foundation of the Key Laboratory of Water Environment Simulation and Treatment in Henan Province(Grant No.2017016).
文摘Based on conventional particle swarm optimization(PSO),this paper presents an efficient and reliable heuristic approach using PSO with an adaptive random inertia weight(ARIW)strategy,referred to as the ARIW-PSO algorithm,to build a multi-objective optimization model for reservoir operation.Using the triangular probability density function,the inertia weight is randomly generated,and the probability density function is automatically adjusted to make the inertia weight generally greater in the initial stage of evolution,which is suitable for global searches.In the evolution process,the inertia weight gradually decreases,which is beneficial to local searches.The performance of the ARIWPSO algorithm was investigated with some classical test functions,and the results were compared with those of the genetic algorithm(GA),the conventional PSO,and other improved PSO methods.Then,the ARIW-PSO algorithm was applied to multi-objective optimal dispatch of the Panjiakou Reservoir and multi-objective flood control operation of a reservoir group on the Luanhe River in China,including the Panjiakou Reservoir,Daheiting Reservoir,and Taolinkou Reservoir.The validity of the multi-objective optimization model for multi-reservoir systems based on the ARIW-PSO algorithm was verified.
基金Acknowledgements： This work was supported by the Foundations of Post Doctor of China （No. 20060401001） and by the Science Research Projects of Ministry of Education of China （No. 06JA630056） and by the Natural Science Foundations of Ningxia （No. NZ0848）.
基金Project supported by the National Natural Science Foundation of China.
文摘In this note, the random weighting approximations for empirical process indexed by abounded class of functions are obtained, and the strong uniform convergence rates of ran-dom weighting empirical processes are given. When unknown multivariate underlingdistributions are not confined by any additional condition, we obtain the random weightingapproximations for multivariate Von Mises statistics and their projection pursuits (PP). Thisresult is also true for the bootstrap approximation of empirical processes.
