[R] Dequantizing

From: Stavros Macrakis <macrakis_at_alum.mit.edu>
Date: Thu, 20 Nov 2008 10:43:27 -0500

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?



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