空间分析(2009-2010-2：3.2)：ESDA(2).ppt

Bihistogram The bihistogram is a tool for assessing whether a before-versus-after modification has caused a change in location; variation; or distribution. 单变量正态QQ图制作步骤： 计算样本平均数 与方差 ； 将样本标准化并排序： 根据标准正态分布，查出下列n个标准正态值： 其中 表示小于该值的标准正态概率值为(2i-1)/2n; 以排序的标准化样本值为横坐标，标准正态值为纵坐标，做（d(i), q(i)）散点图。 加入一条由（q(i)，q(i)）产生的标准正态直线。 示例：Q-Q图 样本：3.93, 1.77, 2.36, 3.2, 2.92 Does the sample come from normal population ? 计算均值和标准差： 计算标准化值 并排序： -1.296, -0.571, 0.102, 0.443, 1.331 根据正态分布表(下页)查n个标准正态值（i=1,2,…,5） q(1)=Z(2i-1)/2n=Z0.1=-1.285, q(2)=Z0.3 =-0.525, q(3)=Z0.5 =0, q(4)=Z0.7 =0.525, q(5)=Z0.9 = 1.285 根据（d(i), q(i)）做图。 加入直线（q(i), q(i)） 。 * * * * * 上图的R代码： # Tight x-axis (so it appears all horizontal lines span infinitely both left and right par(xaxs=i) # Sequence between -3.1 and 3.1 with 0.1 steps x - seq(-3.1, 3.1, 0.1) # Plot a perfect bell curve, or a normal distribution probability density function plot(x, dnorm(x), l, ylim=c(0, 0.5), col=grey, lwd=5) # 100 normally distributed random values with mean 0 and standard deviation 1 rx - rnorm(100) # Add lines that attempt to characterize the distribution probability density for rx # using different bandwidth bw values 0.3, 0.1 and 0.5 (coarse to fine widths) lines(density(rx, bw=0.3), col=#333399) lines(density(rx, bw=0.1), col=#009900) lines(density(rx, bw=0.05), col=#FF6633) # Ticks at bottom to indicate where the random rx values are; add legend rug(rx) legend(topleft, legend=c(reference, 0.3, 0.1, 0.05), bty=n, col=c(grey, #333399, #009900, #FF6633), lwd=c(5, 1, 1, 1)) 3. 核密度估计 带宽h的选择 通常的方法是采用使AMISE (带宽的函数)最小的带宽 AMISE = Asymptotic Mean Integrated Squared Error 一个矛盾 In general, the AMISE still depends of the true underlying density (which of course we dont have!) 解决方法 We need to estimate the AMISE from data as well. This means that the chosen bandwidth is an estimate of an asymptotic approximation. It now sounds as if its too far away fr