How do I deal with ties when using rank-based normalizing transforms, e.g. Blom? I would like to transform heavily skewed data with range (-Inf, Inf) and heavily zero-inflated into a form suitable for using GLMs for significance testing.  Zero-inflation precludes the effective use of standard blom-family transforms (e.g. Blom, Elfving, etc) because they require data not to have ties.  It occurs to me that I can randomly break ties and fit an ensemble of glms on the resulting sampled datasets, and then average the significance result.  Therefore, I have two questions:

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*Is there any theory on normalizing copula transforms for continuous data with ties?  I can't find anything?

*Does this bootstrap-driven correction make sense to folks?  Would it lose statistical power?

Someone has proposed that I run a Wilcoxon test.  That doesn't work for me for two reasons:

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*I need to run some multivariate fits and

*Wilcoxon will heavily extrapolate the significance test by excluding 0s from ranks, which is roughly 2/3 of the measurements (yes, I know, the data sucks, but it's the data)
There's a modified wilcoxon test that addresses this problem but I can't find an implementation (Pratt, J. W. (1959). Remarks on Zeros and Ties in the Wilcoxon Signed Rank Procedures. Journal of the American Statistical Association, 54(287), 655–667. doi:10.1080/01621459.1959.10501526)

Thanks in advance!


Note that spearman p-values are typically at 85th-90th quantile of blom simulations.  Still looking into multivariate predictors, which may benefit from gaussianity.  X-scale: lower is better.  See my last comment above for details.
