In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establi...In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.展开更多
Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of divisio...Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.展开更多
In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices...In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.展开更多
Proper quality planning of limestone raw materials is an essential job of maintaining desired feed in cement plant. Rock-type identification is an integrated part of quality planning for limestone mine. In this paper,...Proper quality planning of limestone raw materials is an essential job of maintaining desired feed in cement plant. Rock-type identification is an integrated part of quality planning for limestone mine. In this paper, a computer vision-based rock-type classification algorithm is proposed for fast and reliable identification without human intervention. A laboratory scale vision-based model was developed using probabilistic neural network（PNN） where color histogram features are used as input. The color image histogram-based features that include weighted mean, skewness and kurtosis features are extracted for all three color space red, green, and blue. A total nine features are used as input for the PNN classification model. The smoothing parameter for PNN model is selected judicially to develop an optimal or close to the optimum classification model. The developed PPN is validated using the test data set and results reveal that the proposed vision-based model can perform satisfactorily for classifying limestone rocktypes. Overall the error of mis-classification is below 6%. When compared with other three classification algorithms, it is observed that the proposed method performs substantially better than all three classification algorithms.展开更多
This paper presents a semiparametric adjustment method suitable for general cases.Assuming that the regularizer matrix is positive definite,the calculation method is discussed and the corresponding formulae are presen...This paper presents a semiparametric adjustment method suitable for general cases.Assuming that the regularizer matrix is positive definite,the calculation method is discussed and the corresponding formulae are presented.Finally,a simulated adjustment problem is constructed to explain the method given in this paper.The results from the semiparametric model and G_M model are compared.The results demonstrate that the model errors or the systematic errors of the observations can be detected correctly with the semiparametric estimate method.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
We prove that two parameter smooth continuous martingales have ∞-modification and establish a Doob’s inequality in terms of(p,r)-capacity for two parameter smooth martingales.
The EWMAcharts are thewell-knownmemory-type charts used formonitoring the small-to-intermediate shifts in the process parameters(location and/or dispersion).The hybrid EWMA(HEWMA)charts are enhanced version of the EWM...The EWMAcharts are thewell-knownmemory-type charts used formonitoring the small-to-intermediate shifts in the process parameters(location and/or dispersion).The hybrid EWMA(HEWMA)charts are enhanced version of the EWMA charts,which effectivelymonitor the process parameters.This paper aims to develop two new uppersided HEWMAcharts for monitoring shifts in process variance,i.e.,HEWMA1 and HEWMA2 charts.The design structures of the proposed HEWMA1 and HEWMA2 charts are based on the concept of integrating the features of two EWMAcharts.TheHEWMA1 and HEWMA2charts plotting statistics are developed using one EWMAstatistic as input for the other EWMAstatistic.AMonte Carlo simulations method is used as a computational technique to determine the numerical results for the performance characteristics,such as average run length(ARL),median run length,and standard deviation run length(SDRL)for assessing the performance of the proposed HEWMA1 and HEWMA2 charts.In addition,to evaluate the overall performance of the proposed HEWMA1 and HEWMA2 charts,other numerical measures consisting of the extra quadratic loss(EQL),relative average run length(RARL),and performance comparison index(PCI)are also computed.The proposed HEWMA1 and HEWMA2 charts are compared to some existing charts,such as CH,CEWMA,HEWMA,AEWMAHHW1,HHW2,AIB-EWMA-I,and AIB-EWMA-II charts,on the basis aforementioned numerical measures.The comparison reveals that the proposed HEWMA1 and HEWMA2 charts achieve better detection ability against the existing charts.In the end,a real-life data application is also provided to enhance the implementation of the proposed HEWMA1 and HEWMA2 charts practically.展开更多
With the use of techniques in nonlinear problems, the IDP (improved discrepancy principle) method has been proposed and applied to the optimal smooth factor (parameterγ) in the inversion process of atmosphere profile...With the use of techniques in nonlinear problems, the IDP (improved discrepancy principle) method has been proposed and applied to the optimal smooth factor (parameterγ) in the inversion process of atmosphere profiles from satellite observation. This method has also been used to inverse atmospheric parameters from the observation of new generation geostationary operational environmental satellite (GOES-8). Results show that this method is more accurate than that in use.展开更多
基金supported by the Natural Science Foundation of China(10771017,10971015,10231030)Key Project to Ministry of Education of the People’s Republic of China(309007)
文摘In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.
文摘Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.
文摘In this article, we introduce the discrete subgroup in ℝ<sup>n</sup> as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝ<sup>n</sup> and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.
文摘Proper quality planning of limestone raw materials is an essential job of maintaining desired feed in cement plant. Rock-type identification is an integrated part of quality planning for limestone mine. In this paper, a computer vision-based rock-type classification algorithm is proposed for fast and reliable identification without human intervention. A laboratory scale vision-based model was developed using probabilistic neural network（PNN） where color histogram features are used as input. The color image histogram-based features that include weighted mean, skewness and kurtosis features are extracted for all three color space red, green, and blue. A total nine features are used as input for the PNN classification model. The smoothing parameter for PNN model is selected judicially to develop an optimal or close to the optimum classification model. The developed PPN is validated using the test data set and results reveal that the proposed vision-based model can perform satisfactorily for classifying limestone rocktypes. Overall the error of mis-classification is below 6%. When compared with other three classification algorithms, it is observed that the proposed method performs substantially better than all three classification algorithms.
文摘This paper presents a semiparametric adjustment method suitable for general cases.Assuming that the regularizer matrix is positive definite,the calculation method is discussed and the corresponding formulae are presented.Finally,a simulated adjustment problem is constructed to explain the method given in this paper.The results from the semiparametric model and G_M model are compared.The results demonstrate that the model errors or the systematic errors of the observations can be detected correctly with the semiparametric estimate method.
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.
文摘We prove that two parameter smooth continuous martingales have ∞-modification and establish a Doob’s inequality in terms of(p,r)-capacity for two parameter smooth martingales.
基金2019 Shanxi Province Soft Science Research Program Project“Research on Sustainable Development Capacity and Classification Construction of Shanxi Development Zone”(Project No.2019041005-2).
文摘The EWMAcharts are thewell-knownmemory-type charts used formonitoring the small-to-intermediate shifts in the process parameters(location and/or dispersion).The hybrid EWMA(HEWMA)charts are enhanced version of the EWMA charts,which effectivelymonitor the process parameters.This paper aims to develop two new uppersided HEWMAcharts for monitoring shifts in process variance,i.e.,HEWMA1 and HEWMA2 charts.The design structures of the proposed HEWMA1 and HEWMA2 charts are based on the concept of integrating the features of two EWMAcharts.TheHEWMA1 and HEWMA2charts plotting statistics are developed using one EWMAstatistic as input for the other EWMAstatistic.AMonte Carlo simulations method is used as a computational technique to determine the numerical results for the performance characteristics,such as average run length(ARL),median run length,and standard deviation run length(SDRL)for assessing the performance of the proposed HEWMA1 and HEWMA2 charts.In addition,to evaluate the overall performance of the proposed HEWMA1 and HEWMA2 charts,other numerical measures consisting of the extra quadratic loss(EQL),relative average run length(RARL),and performance comparison index(PCI)are also computed.The proposed HEWMA1 and HEWMA2 charts are compared to some existing charts,such as CH,CEWMA,HEWMA,AEWMAHHW1,HHW2,AIB-EWMA-I,and AIB-EWMA-II charts,on the basis aforementioned numerical measures.The comparison reveals that the proposed HEWMA1 and HEWMA2 charts achieve better detection ability against the existing charts.In the end,a real-life data application is also provided to enhance the implementation of the proposed HEWMA1 and HEWMA2 charts practically.
文摘With the use of techniques in nonlinear problems, the IDP (improved discrepancy principle) method has been proposed and applied to the optimal smooth factor (parameterγ) in the inversion process of atmosphere profiles from satellite observation. This method has also been used to inverse atmospheric parameters from the observation of new generation geostationary operational environmental satellite (GOES-8). Results show that this method is more accurate than that in use.
