Bootstrapping test

Bootstrapping is a statistical method that uses data resampling with replacement (see: generate_sample_indices) to estimate the robust properties of nearly any statistic. Most commonly, these include standard errors and confidence intervals of a population parameter like a mean, median, correlation coefficient or regression coefficient. Bootstrapping statistics has two attractive attributes:

It is particularly useful when dealing with small sample sizes; It makes no apriori assumption about the distribution of the sample data.

The first rule of data processing is look at your data; the second rule of data processing is understand your data. 

使用Bootstaping test方法检验两个相关系数是否具有显著性差异

nBoot = 1000 ; user set 

nDim = 0 ; or (/0,0/); dimension numbers corresponding to 'N' 

opt = False ; use all default options 

BootStrap =bootstrap_correl(x, y, nBoot, nDim, opt) 

rBoot = BootStrap[0]; bootstrapped cross-correlations inascendingorder 

rBootAvg = BootStrap[1]; Average of the z-transformed bootstrapped cross correlations 

rBootStd = BootStrap[2]; Std. deviation(s) of the z-transformed bootstrapped cross correlations

delete(BootStrap) ; no longer needed 

rBootLow =bootstrap_estimate(rBoot, 0.025, False) ; 2.5% lower confidence bound 

rBootMed =bootstrap_estimate(rBoot, 0.500, False) ; 50.0% median of bootstrapped estimates

绘制直方图：

resr = True

resr@gsnDraw    = False

resr@gsnFrame    = False

resr@gsnHistogramNumberOfBins = 25

resr@tmXBLabelStride = 4

resr@gsFillColor    = "red"

rBoot@long_name  = "Bootstrapped cross-correlations"

hstr    = gsn_histogram(wks, rBoot  ,resr) 

（https://www.ncl.ucar.edu/Applications/Scripts/bootstrap_correl_1.ncl）

使用Bootstaping test方法检验两个均方根误差是否具有显著性差异

nBoot = 10000 

xBoot =new(nBoot, typeof(x)) 

do ns=0,nBoot-1 ; generate multiple estimates 

    iw =generate_sample_indices(N,1) ; indices with replacement 

    xBoot(ns) =dim_avg_n( x(iw), 0 ) ; compute average 

end do 

xAvgBoot =dim_avg_n(xBoot,0) ; Averages of bootstrapped samples 

xStdBoot =dim_stddev_n(xBoot,0) ; Std Dev " " " 

xStdErrBoot = xStdBoot/nBoot ; Std. Error of bootstrapped estimates 

ia =dim_pqsort_n(xBoot, 2, 0) ; sort bootstrap means into ascending order 

n025 =round(0.025*(nBoot-1),3) ; indices for sorted array 

n500 =round(0.500*(nBoot-1),3) 

n975 =round(0.975*(nBoot-1),3) 

xBoot_025= xBoot(n025) ; 2.5% level 

xBoot_500= xBoot(n500) ; 50.0% level (median) 

xBoot_975= xBoot(n975) ; 97.5% level

结合上面绘制直方图。

参考：

https://www.ncl.ucar.edu/Applications/bootstrap.shtml

Statistical methods for the analysis of simulated and observed climate data Barbara Hennemuth et al (2013) Applied in projects and institutions dealing with climate change impact and adaptationCSC Report 13 (一本比较好的气候数据统计书)