In this paper, we establish some maximal inequalities for demimartingales which generalize and improve the results of Christofides. The maximal inequalities for demimartingales are used as key inequalities to establis...In this paper, we establish some maximal inequalities for demimartingales which generalize and improve the results of Christofides. The maximal inequalities for demimartingales are used as key inequalities to establish other results including Doob’s type maximal inequality for demimartingales, strong laws of large numbers and growth rate for demimartingales and associated random variables. At last, we give an equivalent condition of uniform integrability for demisubmartingales.展开更多
Consider the following heteroscedastic semiparametric regression model：where {Xi, 1 〈 i 〈 n} are random design points, errors {ei, 1 〈 i 〈 n} are negatively associated （NA） random variables, （r2 = h（ui）, and...Consider the following heteroscedastic semiparametric regression model：where {Xi, 1 〈 i 〈 n} are random design points, errors {ei, 1 〈 i 〈 n} are negatively associated （NA） random variables, （r2 = h（ui）, and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g（t） and the variance function h（u） are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O（n- 1 log n）. Hence our results are extensions of those re, sults on independent random error settings.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
The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effe...The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effect on the flow and material transport has been emphasized, and a thirty-year mean value of wind has been considered in the numerical simulation. As a whole, even after the reclaiming and dredging are conducted, the flow pattern looks similar to the original state. However, velocity variations up to 20% to 100% appear in the vicinity of the construction area. In the case of summcr wind forcing, the seawater exchange rate increases from 71.6% to 82.9% after the reclaiming and dredging, as indicated by a particle-tracking method. On the contrary, in the case of winter wind forcing, thc seawater cxchange rate appears to be 97.2% under natural conditions but decrcases slightly to 93.2% aftcr the rcclaiming and dredging. Thus, the wind forcing plays an important role in controlling the seawater exchangc rates. The seawater cxchange rate is further improved by 15% if the dredging is simultaneously carried out with the reclaiming. This suggests that the dredging can be an effective means to mitigate the variation of flow.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 10871001, 60803059)the Innovation Group Foundation of Anhui University
文摘In this paper, we establish some maximal inequalities for demimartingales which generalize and improve the results of Christofides. The maximal inequalities for demimartingales are used as key inequalities to establish other results including Doob’s type maximal inequality for demimartingales, strong laws of large numbers and growth rate for demimartingales and associated random variables. At last, we give an equivalent condition of uniform integrability for demisubmartingales.
基金supported by the National Natural Science Foundation of China (No. 11071022)the Key Project of the Ministry of Education of China (No. 209078)the Youth Project of Hubei Provincial Department of Education of China (No. Q20122202)
文摘Consider the following heteroscedastic semiparametric regression model：where {Xi, 1 〈 i 〈 n} are random design points, errors {ei, 1 〈 i 〈 n} are negatively associated （NA） random variables, （r2 = h（ui）, and {ui} and {ti} are two nonrandom sequences on [0, 1]. Some wavelet estimators of the parametric component β, the non- parametric component g（t） and the variance function h（u） are given. Under some general conditions, the strong convergence rate of these wavelet estimators is O（n- 1 log n）. Hence our results are extensions of those re, sults on independent random error settings.
文摘针对传统地下采场开挖稳定评估方法存在的局限性,引入机器学习方法,提出基于随机森林算法(Random forest,RF)和K-最近邻算法(K-nearest neighbor,KNN)的地下采场开挖稳定性预测模型.以加拿大8个采场为例,首先,获取并分析399组观测数据,其中涵盖了相应的岩石质量分级(Rock Mass Rating,RMR)值、跨度以及对应的稳定、潜在不稳定或不稳定状态.然后将地下采场的稳定性程度进行三分类及二分类,采用10折交叉验证方法进行模型超参数优化,在不作任何假设的前提下,捕捉地下采场开挖稳定性与RMR值、跨度之间的复杂关系.研究表明:二分类结果准确性高于三分类预测结果;在二分类方式下,两种算法的准确率及召回率均高于90%,其中KNN算法的表现优于RF算法;提出的两种方法较先前研究的正确率有很大提升,为开挖稳定性评估提供了可靠途径.
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.
文摘The flow and seawater exchange rates have been predicted using a two-dimensional numerical model and a Lagrangian method for a semi-enclosed shallow bay where reclaiming and dredging works are scheduled. The wind effect on the flow and material transport has been emphasized, and a thirty-year mean value of wind has been considered in the numerical simulation. As a whole, even after the reclaiming and dredging are conducted, the flow pattern looks similar to the original state. However, velocity variations up to 20% to 100% appear in the vicinity of the construction area. In the case of summcr wind forcing, the seawater exchange rate increases from 71.6% to 82.9% after the reclaiming and dredging, as indicated by a particle-tracking method. On the contrary, in the case of winter wind forcing, thc seawater cxchange rate appears to be 97.2% under natural conditions but decrcases slightly to 93.2% aftcr the rcclaiming and dredging. Thus, the wind forcing plays an important role in controlling the seawater exchangc rates. The seawater cxchange rate is further improved by 15% if the dredging is simultaneously carried out with the reclaiming. This suggests that the dredging can be an effective means to mitigate the variation of flow.
