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Optimization of variance-stabilizing transformations




Abstract
Variance-stabilizing transformations are commonly exploited in order to make exotic data easily tractable by standard methods. However, for the most common families of distributions (e.g., binomial, Poisson, etc.) exact stabilization is not possible and even achieving some approximate stabilization turns out to be rather challenging.
We approach the variance stabilization problem as an explicit optimization problem and propose recursive procedures to minimize a nonlinear stabilization functional that measures the discrepancy between the standard deviation of the transformed variables and a fixed desired constant. Further, we relax the typical requirement of monotonicity of the transformation and introduce optimized nonmonotone stabilizers which are nevertheless invertible in terms of expectations.
We demonstrate a number of optimized variance-stabilizing transformations for the most common distribution families. These stabilizers are shown to outperform the existing ones. In particular, optimized variance-stabilizing transformations for low-count Poisson, binomial, and negative-binomial data are presented.


TRANSFORMATIONS REFERENCES

f(x) Transformations
Examples are for the following one-parameter families of distributions:
  - Binomial
  - Negative binomial
  - Poisson
  - Filtered Poisson by 5x5 2-D B3-spline filter
  - Clipped heteroskedastic normal

ReadMe.txt
Information and instructions 		Optimized variance-stabilizing transformations

download zip package
8-Mbyte zip-file
includes
Matlab MAT-file (ver. 5 or later) and
16-digit ASCII (double precision) formats

released July 1, 2009

 		transformations for the negative binomial exponent=10


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References References

PDF Foi, A., “Optimization of variance-stabilizing transformations”, preprint, 2009.

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