I have some data measured with a coarsely-quantized clock. Let's say
the real data are
q<- sort(rexp(100,.5))
The quantized form is floor(q), so a simple quantile plot of one
against the other can be calculated using:
plot(q,type="l"); points(floor(q),col="red")
which of course shows the characteristic stair-step. I would like to
smooth the quantized form back into an approximation of the underlying
data.
The simplest approach I can think of adds a uniform random variable of
the size of the quantization:
plot(q,type="l"); points(floor(q),col="red");
points(floor(q)+runif(100,0,1),col="blue")
This gives pretty good results for uniform distributions, but less
good for others (like exponential). Is there a better
interpolation/smoothing function for cases like this, either Monte
Carlo as above or deterministic?
Thanks,
-s
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