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
利用OMI数据反演得到的多时相NO2浓度产話(空间分辨率为0.125°X0.125°),分析了2005-2017年西南地区四省市(云南省、贵州省、四川省及重庆市)对流层NO2柱浓度的时空分布特征,并对其影响因素进行了简单分析。结果表明:(1)2005-2...利用OMI数据反演得到的多时相NO2浓度产話(空间分辨率为0.125°X0.125°),分析了2005-2017年西南地区四省市(云南省、贵州省、四川省及重庆市)对流层NO2柱浓度的时空分布特征,并对其影响因素进行了简单分析。结果表明:(1)2005-2017年间,西南地区NO2柱浓度年均值较小,13年的年均值为1.8015 x 10^15molec/cm^2.年变化整体表现为先增大后减小趋势;季节变化表现为:冬季〉秋季〉春季〉夏季,而月变化呈内凹型分布;(2)空间分布上呈东部高、西部低的特点,并且跨度较大,四川省东部和重庆市西部地区的NO2柱浓度年均值大于10.0 x 10^15molec/cm^2,而四川省西部和云南省中西部地区的NO2柱浓度低于1.0 X 10^15molec/cm^2;(3)云南省的NO2柱浓度最低,重庆市的NO2柱浓度远远高于其他3个省;此外,云南省的年变化最为平缓,而重庆市的变化幅度最大;(4)研究区的地理位置及地形特征、气象要素、人口密集度及经济发展状况等因素都直接影响对流层NO2柱浓度的时空分布。展开更多
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.
文摘利用OMI数据反演得到的多时相NO2浓度产話(空间分辨率为0.125°X0.125°),分析了2005-2017年西南地区四省市(云南省、贵州省、四川省及重庆市)对流层NO2柱浓度的时空分布特征,并对其影响因素进行了简单分析。结果表明:(1)2005-2017年间,西南地区NO2柱浓度年均值较小,13年的年均值为1.8015 x 10^15molec/cm^2.年变化整体表现为先增大后减小趋势;季节变化表现为:冬季〉秋季〉春季〉夏季,而月变化呈内凹型分布;(2)空间分布上呈东部高、西部低的特点,并且跨度较大,四川省东部和重庆市西部地区的NO2柱浓度年均值大于10.0 x 10^15molec/cm^2,而四川省西部和云南省中西部地区的NO2柱浓度低于1.0 X 10^15molec/cm^2;(3)云南省的NO2柱浓度最低,重庆市的NO2柱浓度远远高于其他3个省;此外,云南省的年变化最为平缓,而重庆市的变化幅度最大;(4)研究区的地理位置及地形特征、气象要素、人口密集度及经济发展状况等因素都直接影响对流层NO2柱浓度的时空分布。
