如何使用R获得LOWESS拟合的置信区间? [英] How to get the confidence intervals for LOWESS fit using R?

问题描述

对于R的统计"数据包的LOWESS回归线的置信区间(CI)，我找不到任何令人满意的答案:

I didn't find any satisfactory answer to the confidence intervals (CIs) for LOWESS regression line of the 'stats' package of R:

plot(cars, main = "lowess(cars)")
lines(lowess(cars), col = 2)

但是我不确定如何围绕它绘制95％的CI?但是，我知道我可以从中获取估计的差异

But I'm unsure how to draw a 95% CI around it?? However, I know I could get the estimated variance from

V = s^2*sum(w^2)

其中，s2 =估计误差方差，w =应用于X的权重.因此，95％CI应该是

where, s2= estimated error variance, and w=weights applied to the X. Therefore, the 95% CIs should be

Y plus/minus 2*sqrt(V(Y))

我知道有一种方法可以使黄土适合CI，但是我更喜欢LOWESS，因为它很坚固.感谢您的建议.

I know there's a way of getting the CIs from loess fit, but I'd rather prefer LOWESS because it is robust. Thanks for your suggestions.

推荐答案

您可以使用predict()和loess()进行此操作. lowess比loess更旧，并且功能较少，但速度更快.但是在这种情况下，我将按以下方式使用loess.

You can do this with predict() and loess(). lowess is older than loess and has fewer features, though it is a bit faster. But in this context, I'd use loess as follows.

plot(cars)
plx<-predict(loess(cars$dist ~ cars$speed), se=T)

lines(cars$speed,plx$fit)
lines(cars$speed,plx$fit - qt(0.975,plx$df)*plx$se, lty=2)
lines(cars$speed,plx$fit + qt(0.975,plx$df)*plx$se, lty=2)

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