随着2020年新冠肺炎疫情在全球肆虐,国际环境动荡加剧引发了大众对于粮食储备问题的担忧,而及时估算种植面积对于有效应对可能的突发事件具有重要战略意义。考虑到粮食种植具有范围广、区域差异大的特点,因而进行面积估算时,混合效应模...随着2020年新冠肺炎疫情在全球肆虐,国际环境动荡加剧引发了大众对于粮食储备问题的担忧,而及时估算种植面积对于有效应对可能的突发事件具有重要战略意义。考虑到粮食种植具有范围广、区域差异大的特点,因而进行面积估算时,混合效应模型是非常合适的选择,但现有文献多局限于解决有抽样单元的剩余区域的外推估算问题,对零样本量的域估计问题则鲜有涉及。值得注意的是,在进行农业抽样工作时,抽样数量的设计多服务于国家或省级层面,对于人口数量较少或经济程度不发达的地区,则容易出现没有样本被抽中的情况。往往这类地区是以农业为主要产业,因此忽视该类地区的农作物面积将会对我国实现农业精准监测产生显著影响。有鉴于此,本文提出使用改良后的分类混合效应模型预测方法(Modified Classified Mixed Model Prediction,MCMMP),其原理可概述如下:首先通过协变量信息对抽样单元进行聚类,然后使用混合效应模型预测所有类的随机效应,最后利用待估单元所处类的随机效应对待估单元面积进行估算。为展示MCMMP的应用潜力,本文基于山东省济宁市兖州区下属12个镇的卫星图像已经部分测绘数据,并结合“留一法”对小麦种植面积进行了估算。结果显示与现有方法相比,MCMMP具有更小的相对误差,且当感兴趣的变量为小域均值时,如村或镇范围的平均土地面积时,MCMMP依旧表现最优。展开更多
Consider a stable AR model of two parameter spatial series {X<sub>t</sub>, t∈N<sup>2</sup>}, i. e. {X<sub>t</sub>t∈N<sup>2</sup>} is homogeneous and satisfies the foll...Consider a stable AR model of two parameter spatial series {X<sub>t</sub>, t∈N<sup>2</sup>}, i. e. {X<sub>t</sub>t∈N<sup>2</sup>} is homogeneous and satisfies the following difference equationX<sub>t</sub>-sum from n=s∈【v,p] to a<sub>s</sub>X<sub>t-s</sub>=W<sub>t</sub> （t∈N<sup>2</sup>）where {W<sub>t</sub>, t∈N<sup>2</sup>} is a two parameter white noise and the notation【3, p] expresses the set of two dimentional lattice points {（k<sub>1</sub>, k<sub>2</sub>）: 0≤k<sub>1</sub>≤p<sub>1</sub>, 0≤k<sub>2</sub>≤p<sub>2</sub> but （k<sub>1</sub>, k<sub>2</sub>）≠（0, 0）}, and furthermore the two-variable polynomial1-sum from n=（s<sub>1</sub>,s<sub>2</sub>）∈【0,p] a（s<sub>1</sub>,s<sub>2</sub>） Z<sub>1</sub><sup>k</sup><sub>1</sub>Z<sub>2</sub><sup>s</sup><sub>2</sub>≠0（|Z<sub>1</sub>|≤1,|Z<sub>2</sub>|≤1）.In this paper, under frirly general conditions （it is required that {W<sub>t</sub>} Satisfies the conditions of two-parameter martingale difference, which is much weaker than supposing {W<sub>t</sub>} to be i. i. d.）, the author obtains strong consistency and asymptotic normality of the Y-W （LS） estimate of the AR parameters {a<sub>s</sub>} whenever n<sub>1</sub>n<sub>2</sub>→∞, where n<sub>1</sub> and denote the horizontal and vertical sampling width respectively.展开更多
In this paper,some results in [1] on parameter estimation of spatial AR models are improved.Moreover,using some recent results on convergence rate of sample autocorrelations,we give strongly consistent order estimates...In this paper,some results in [1] on parameter estimation of spatial AR models are improved.Moreover,using some recent results on convergence rate of sample autocorrelations,we give strongly consistent order estimates for spatial AR models and iterated logarithmic convergence rate for AR parameter estimates, which improve the result in [2] of weakly consistent order estimation and strongly consistent parameter estimation.展开更多
文摘随着2020年新冠肺炎疫情在全球肆虐,国际环境动荡加剧引发了大众对于粮食储备问题的担忧,而及时估算种植面积对于有效应对可能的突发事件具有重要战略意义。考虑到粮食种植具有范围广、区域差异大的特点,因而进行面积估算时,混合效应模型是非常合适的选择,但现有文献多局限于解决有抽样单元的剩余区域的外推估算问题,对零样本量的域估计问题则鲜有涉及。值得注意的是,在进行农业抽样工作时,抽样数量的设计多服务于国家或省级层面,对于人口数量较少或经济程度不发达的地区,则容易出现没有样本被抽中的情况。往往这类地区是以农业为主要产业,因此忽视该类地区的农作物面积将会对我国实现农业精准监测产生显著影响。有鉴于此,本文提出使用改良后的分类混合效应模型预测方法(Modified Classified Mixed Model Prediction,MCMMP),其原理可概述如下:首先通过协变量信息对抽样单元进行聚类,然后使用混合效应模型预测所有类的随机效应,最后利用待估单元所处类的随机效应对待估单元面积进行估算。为展示MCMMP的应用潜力,本文基于山东省济宁市兖州区下属12个镇的卫星图像已经部分测绘数据,并结合“留一法”对小麦种植面积进行了估算。结果显示与现有方法相比,MCMMP具有更小的相对误差,且当感兴趣的变量为小域均值时,如村或镇范围的平均土地面积时,MCMMP依旧表现最优。
文摘Consider a stable AR model of two parameter spatial series {X<sub>t</sub>, t∈N<sup>2</sup>}, i. e. {X<sub>t</sub>t∈N<sup>2</sup>} is homogeneous and satisfies the following difference equationX<sub>t</sub>-sum from n=s∈【v,p] to a<sub>s</sub>X<sub>t-s</sub>=W<sub>t</sub> （t∈N<sup>2</sup>）where {W<sub>t</sub>, t∈N<sup>2</sup>} is a two parameter white noise and the notation【3, p] expresses the set of two dimentional lattice points {（k<sub>1</sub>, k<sub>2</sub>）: 0≤k<sub>1</sub>≤p<sub>1</sub>, 0≤k<sub>2</sub>≤p<sub>2</sub> but （k<sub>1</sub>, k<sub>2</sub>）≠（0, 0）}, and furthermore the two-variable polynomial1-sum from n=（s<sub>1</sub>,s<sub>2</sub>）∈【0,p] a（s<sub>1</sub>,s<sub>2</sub>） Z<sub>1</sub><sup>k</sup><sub>1</sub>Z<sub>2</sub><sup>s</sup><sub>2</sub>≠0（|Z<sub>1</sub>|≤1,|Z<sub>2</sub>|≤1）.In this paper, under frirly general conditions （it is required that {W<sub>t</sub>} Satisfies the conditions of two-parameter martingale difference, which is much weaker than supposing {W<sub>t</sub>} to be i. i. d.）, the author obtains strong consistency and asymptotic normality of the Y-W （LS） estimate of the AR parameters {a<sub>s</sub>} whenever n<sub>1</sub>n<sub>2</sub>→∞, where n<sub>1</sub> and denote the horizontal and vertical sampling width respectively.
基金This project is supported by the Doctoral Programme Foundation of Institute of Higher Educationby the National Natural Science Foundation of China
文摘In this paper,some results in [1] on parameter estimation of spatial AR models are improved.Moreover,using some recent results on convergence rate of sample autocorrelations,we give strongly consistent order estimates for spatial AR models and iterated logarithmic convergence rate for AR parameter estimates, which improve the result in [2] of weakly consistent order estimation and strongly consistent parameter estimation.
