Hello,
I am fitting data using different methods e.g. Local Polynomial and Smoothing
splines. The data is generated out of a true function model with added normally
distributed noise.
I would like to know "how often the confidence band for all points
simultaneously contain all true values". I can answer the question for one
point in the following way:
e.g.
#
=========================================================================================
# How many times the pointwise confidence interval at x=0.5 contains the true
value at 0.5
# i.e. what is the so called "coverage rate"?
#
=========================================================================================
pos = which(x==0.5)
sum(abs(estlp[pos,] - m(x[pos])) <= 1.96*selp[pos,]) # equidistant x outputs
946
# non-equidistant x
outputs 938
sum(abs(estss[pos,] - m(x[pos])) <= 1.96*sess[pos,]) # equidistant x outputs
895
# non-equidistant x
outputs 936
This basically tells me that out of 1000 simulation runs with different random
noise, 946 times the true value i.e. m(x) for x=0.5 is contained within the 95%
confidence interval. The estlp Local Polynomial performs better than Smoothing
Splines under this criteria ...
Now is there any specific way to answer "how often the confidence band for all
points simultaneously contain all true values" other than this below?
#
=========================================================================================
# How often does the confidence band for all points simultaneously contain all
true values?
#
=========================================================================================
sum(abs(estlp[,] - m(x[])) <= 1.96*selp[,]) # equidistant x outputs
92560
# non-equidistant x
outputs 92109
sum(abs(estss[,] - m(x[])) <= 1.96*sess[,]) # equidistant x outputs
90804
# non-equidistant x
outputs 94641
Is there a dedicated function in R for this purpose i.e. to build confidence
bands around a given fit ... maybe a way to plot it nicely too given that the
Estimated SE are calculated.
Many thanks in advance,
Best regards,
Giovanni
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