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So, I have some idea how to smooth a set of points to produce a smooth estimate of the conditional mean.

Suppose that I want to estimate the standard deviation locally. That is, I have a set of points (x,y) and in different regions of the x space, the standard deviation of y might vary. I would like to produce a smooth estimate of the standard deviation.

My guess would be to do something like nearest neighbours. So, at every value of x, pick the 10 nearest points, say, and calculate the standard deviation.

Is that right? Is there any theory that bears on this?

I suppose answers will apply to any statistic, not just the s.d., but I chose the s.d. because it clearly has to be calculated from more than just individual points.

dash2
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  • bootstrap resampling, Mann-Kendall, relates to the variance through the Delta method. Bollinger is also not bad - but it depends on the nature of your data, and whether "x" is time. – EngrStudent Sep 17 '15 at 17:52

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