样本正态分布对降低空间抽样数量的重要性
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摘要
样本总体的分布特征是影响抽样样本数量的主要因素,对于样本总体为非正态分布的情况,正态转换是降低抽样样本数量、提高抽样调查效率的有效手段。笔者采用中国大陆区域2005年耕地空间分布数据,以1:10万地形图图幅框作为抽样单元,统计每个图幅框内耕地面积占比。分别采样1.5次开方、2次开方、2.5次开方、3次开方和4次开方运算的方式对原始数据进行正态转换。在此基础上对比分析了转换前后数据的峰度及偏度、抽样个数及抽样结果误差等。结果表明,基于2.5次开方运算后的分层抽样可以大大降低抽样率,由92.26%降低为22.55%,耕地面积指数平均值相对误差由7.06%降低为5.66%。利用2015年耕地面积指数进行抽样方法的精度检验,抽样平均值相对误差仅为3.27%。研究提出的抽样方法具有较高的适用性,同时也表明空间抽样中数据分布正态转换是非常必要的。本研究成果为广大学者在空间抽样调查方面的研究提供了有益的借鉴。
The general distribution feature of samples is a major factor to impact sample size, and normal transformation for non-normal distribution of general samples is an effective mean to reduce sample size and improve survey efficiency. By using the spatial distribution data of the cultivated land in Chinese mainland in2005 and taking 1:100000 topographic map frames as sampling units, we calculated the proportion of cultivated land area in each map frames, and conducted the normal transformation of original data by calculating 1.5 times square root, 2 times square root, 2.5 times square root, 3 times square root, and 4 times square root of them. Based on above transformation, we carried out the contrastive analysis on the factors of kurtosis and skewness, the sample size and sampling error before and after the transformation. The result showed that: the stratified sampling based on 2.5 square root operation could dramatically reduce sampling rate; the sampling rate was reduced from 92.26% to 22.55%, and the average relative error of cultivated area index was reduced from 7.06% to 5.66%. The accuracy of sampling method was verified by using the cultivated land area index in 2015, and the average relative error of the sampling was only 3.27%. The sampling method proposed by the study is highly applicable, and it is necessary to make normal transformation on the data distribution in spatial sampling. The results can provide reference for the scholars on spatial sampling survey.
The general distribution feature of samples is a major factor to impact sample size, and normal transformation for non-normal distribution of general samples is an effective mean to reduce sample size and improve survey efficiency. By using the spatial distribution data of the cultivated land in Chinese mainland in2005 and taking 1:100000 topographic map frames as sampling units, we calculated the proportion of cultivated land area in each map frames, and conducted the normal transformation of original data by calculating 1.5 times square root, 2 times square root, 2.5 times square root, 3 times square root, and 4 times square root of them. Based on above transformation, we carried out the contrastive analysis on the factors of kurtosis and skewness, the sample size and sampling error before and after the transformation. The result showed that: the stratified sampling based on 2.5 square root operation could dramatically reduce sampling rate; the sampling rate was reduced from 92.26% to 22.55%, and the average relative error of cultivated area index was reduced from 7.06% to 5.66%. The accuracy of sampling method was verified by using the cultivated land area index in 2015, and the average relative error of the sampling was only 3.27%. The sampling method proposed by the study is highly applicable, and it is necessary to make normal transformation on the data distribution in spatial sampling. The results can provide reference for the scholars on spatial sampling survey.
引文
[1]陈仲新,刘海启,周清波,等.全国冬小麦面积变化遥感监测抽样外推方法的研究[J].农业工程学报,2000,16(5):126-129.
[2]钱永兰,杨邦杰,焦险峰.基于遥感抽样的国家尺度农作物面积统计方法评估[J].农业工程学报,2007,23(11):180-187.
[3]陈水森,柳钦火,陈良富,等.粮食作物播种面积遥感监测研究进展[J].农业工程学报,2005,21(6):166-171.
[4]申克建,何浩,蒙红卫,等.农作物面积空间抽样调查研究进展[J].中国农业资源与区划,2012,33(4):11-16.
[5]张锦水,潘耀忠,胡潭高,等.冬小麦种植面积空间抽样效率影响因子分析[J].农业工程学报,2009,25(8):169-173.
[6]徐迪峰,徐锐.基于空间抽样的农作物面积遥感测量[J].北京测绘,2009,4:40-42,55.
[7]雷燕飞.基于历史影像的冬小麦种植面积抽样方法研究[D].北京:北京师范大学,2009.
[8]李连发.空间抽样模型研究[D].北京:中国科学院地理科学与资源研究所,2001.
[9]易嫦.基于中分辨率遥感影像的冬小麦种植面积空间抽样调查方法研究[D].北京:北京师范大学,2008.
[10]蔡德文.基于遥感与抽样技术的新疆棉花种植面积提取[D].北京:中国科学院研究生院,2012.
[11]胡永森.多尺度遥感数据结合空间抽样方法的大区域作物面积估算[D].抚州:东华理工大学,2016.
[12]阳小琼,朱文泉,潘耀忠,等.作物种植面积空间对地抽样方法设计[J].农业工程学报,2007,23(12):150-155.
[13]刘建红,朱文泉.耕地变化空间抽样调查方案的精度与效率分析[J].农业工程学报,2010,26(10):331-336.
[14]张焕雪,李强子,文宁,等.农作物种植面积遥感抽样调查的误差影响因素分析[J].农业工程学报,2014,30(13):176-184.
[15]李琳一,袁涛,陈旭.农业抽样调查中统计理论和抽样方法选取研究[J].上海农业学报,2011,27(4):5-8.16] Yang J, Yue Y, Song H, et al. Sampling and optimizing methods of cultivated land quality based on spatial simulated annealing algorithm[J]. Transactions of the Chinese Society of Agricultural Engineering,2015,31(20):253-261.
[17] Wu Q, Pei Z, Wang F, et al. A Sampling Design for Monitoring of the Cultivated Areas of Main Crops at National Scale Based 3S Technologies in China[M]. Computer and Computing Technologies in Agriculture VI. Springer Berlin Heidelberg,2016:10-19.
[18]郑菊.农业抽样调查中统计理论和抽样方法选取研究[J].中国农业信息(上半月),2014,13:115-115.
[19] Boryan C, Yang Z W, Mueller R, et al. Monitoring US agriculture:the US department of agriculture, national agricultural statistics service, cropland data layer program[J]. Geocarto International,2011,26(5):341-358.
[20] Gallego F J. Crop area estimation in the mars project[C].Conference on ten years of the MARS Project, Brussels, April,1999.
[21] Carfagna E, Gallego F J. Using remote sensing for agricultural statistics[J]. International Statistical Review,2005,73(3):389-404.
[22] Delince J, Taylor J, Sannier C, et al. Regional crop inventories in Europe assisted by remote sensing:1988-1993[R]. Regional Inventories Synthesis Report,1997.
[23] Jacques P, Gallego J. The LUCAS 2006 project-A new methodology[M]. Eurostat,2006.
[24] Tsiligirides T A. Remote sensing as a tool for agricultural statistics:a case study of area frame sampling methodology in Hellas[J]. Computers&Electronics in Agriculture,1998,20(1):45-77.
[25] DelincéJ. A European approach to area frame survey[J].Proceedings of the Conference on Agricultural and Environmental Statistical Applications in Rome(CAESAR),2001,2:463-472.
[26]宫野.正态分布的抽样方法[J].计算物理,1997,14(4/5):566-568.
[27]高永久.样本均值作为总体均值估计量的合理性[J].长春理工大学学报:自然科学版,2008,31(4):158-159.
[28]王学民.关于样本均值的抽样分布能否作正态近似的探讨[J].统计研究,2005,22(7):75-78.
[29]崔书华,李果,刘军虎,等.基于偏度与峰度的数据质量评估[J].弹箭与制导学报,2015,35(6):98-100,105.
[30]金勇进,杜子芳,蒋妍.抽样技术[M].北京:中国人民大学出版社,2000.
[31]李金昌.应用抽样技术[M].北京:科学出版社,2006.
[32]杜子芳.抽样技术及其应用[M].北京:清华大学出版社,2005.
[2]钱永兰,杨邦杰,焦险峰.基于遥感抽样的国家尺度农作物面积统计方法评估[J].农业工程学报,2007,23(11):180-187.
[3]陈水森,柳钦火,陈良富,等.粮食作物播种面积遥感监测研究进展[J].农业工程学报,2005,21(6):166-171.
[4]申克建,何浩,蒙红卫,等.农作物面积空间抽样调查研究进展[J].中国农业资源与区划,2012,33(4):11-16.
[5]张锦水,潘耀忠,胡潭高,等.冬小麦种植面积空间抽样效率影响因子分析[J].农业工程学报,2009,25(8):169-173.
[6]徐迪峰,徐锐.基于空间抽样的农作物面积遥感测量[J].北京测绘,2009,4:40-42,55.
[7]雷燕飞.基于历史影像的冬小麦种植面积抽样方法研究[D].北京:北京师范大学,2009.
[8]李连发.空间抽样模型研究[D].北京:中国科学院地理科学与资源研究所,2001.
[9]易嫦.基于中分辨率遥感影像的冬小麦种植面积空间抽样调查方法研究[D].北京:北京师范大学,2008.
[10]蔡德文.基于遥感与抽样技术的新疆棉花种植面积提取[D].北京:中国科学院研究生院,2012.
[11]胡永森.多尺度遥感数据结合空间抽样方法的大区域作物面积估算[D].抚州:东华理工大学,2016.
[12]阳小琼,朱文泉,潘耀忠,等.作物种植面积空间对地抽样方法设计[J].农业工程学报,2007,23(12):150-155.
[13]刘建红,朱文泉.耕地变化空间抽样调查方案的精度与效率分析[J].农业工程学报,2010,26(10):331-336.
[14]张焕雪,李强子,文宁,等.农作物种植面积遥感抽样调查的误差影响因素分析[J].农业工程学报,2014,30(13):176-184.
[15]李琳一,袁涛,陈旭.农业抽样调查中统计理论和抽样方法选取研究[J].上海农业学报,2011,27(4):5-8.16] Yang J, Yue Y, Song H, et al. Sampling and optimizing methods of cultivated land quality based on spatial simulated annealing algorithm[J]. Transactions of the Chinese Society of Agricultural Engineering,2015,31(20):253-261.
[17] Wu Q, Pei Z, Wang F, et al. A Sampling Design for Monitoring of the Cultivated Areas of Main Crops at National Scale Based 3S Technologies in China[M]. Computer and Computing Technologies in Agriculture VI. Springer Berlin Heidelberg,2016:10-19.
[18]郑菊.农业抽样调查中统计理论和抽样方法选取研究[J].中国农业信息(上半月),2014,13:115-115.
[19] Boryan C, Yang Z W, Mueller R, et al. Monitoring US agriculture:the US department of agriculture, national agricultural statistics service, cropland data layer program[J]. Geocarto International,2011,26(5):341-358.
[20] Gallego F J. Crop area estimation in the mars project[C].Conference on ten years of the MARS Project, Brussels, April,1999.
[21] Carfagna E, Gallego F J. Using remote sensing for agricultural statistics[J]. International Statistical Review,2005,73(3):389-404.
[22] Delince J, Taylor J, Sannier C, et al. Regional crop inventories in Europe assisted by remote sensing:1988-1993[R]. Regional Inventories Synthesis Report,1997.
[23] Jacques P, Gallego J. The LUCAS 2006 project-A new methodology[M]. Eurostat,2006.
[24] Tsiligirides T A. Remote sensing as a tool for agricultural statistics:a case study of area frame sampling methodology in Hellas[J]. Computers&Electronics in Agriculture,1998,20(1):45-77.
[25] DelincéJ. A European approach to area frame survey[J].Proceedings of the Conference on Agricultural and Environmental Statistical Applications in Rome(CAESAR),2001,2:463-472.
[26]宫野.正态分布的抽样方法[J].计算物理,1997,14(4/5):566-568.
[27]高永久.样本均值作为总体均值估计量的合理性[J].长春理工大学学报:自然科学版,2008,31(4):158-159.
[28]王学民.关于样本均值的抽样分布能否作正态近似的探讨[J].统计研究,2005,22(7):75-78.
[29]崔书华,李果,刘军虎,等.基于偏度与峰度的数据质量评估[J].弹箭与制导学报,2015,35(6):98-100,105.
[30]金勇进,杜子芳,蒋妍.抽样技术[M].北京:中国人民大学出版社,2000.
[31]李金昌.应用抽样技术[M].北京:科学出版社,2006.
[32]杜子芳.抽样技术及其应用[M].北京:清华大学出版社,2005.