Tim,
  The NADA package has the cenken function, which claims that it treats
multiple detection limits as Philip described. Try that instead. NADA does
not have a seasonal Kendall test.
  The U.S. Geological Survey has prototype packages available on gitHub.
The USGSwsQW package has a function called kendallATS.test that does what
the cenken function in NADA does, but has an option for dealing with
missing values. It also reports taub (corrected for ties) rather than tau
and uses Akritas' original solver for the slope estimate, if that is
important. We also have a package called restrend, which has the censSeaken
function, that does the seasonal Kendall test on multiply censored data. It
has not yet been built for R 3.1. But I can do that if you need that test.
Dave
P.S. These packages will eventually be released on CRAN, but require a
formal publication before we can do that.



On Mon, Jul 28, 2014 at 7:17 AM, Dixon, Philip M [STAT] <pdixon@iastate.edu>
wrote:

> Tim,
>
> The issue with multiple detection limits with Kendall's tau or the
> Seasonal Mann-Kendall variation is computational, not conceptual.  The
> strong advantage of Kendall's tau, over rank-based methods, is that tau
> handles multiple detection limits in a common-sense way.  The pair (5, 10)
> can be ranked, the pair (<5, 10) can be ranked, the pair (<5, 3) can not be
> ranked, and the pair (<5, <6) can not be ranked.  Having said this, I don't
> believe either the NADA or the current version of EnvStats implementations
> handles multiple detection limits.  I've always done this by hand when
> needed, but that code is written for specific data sets and unlikely to be
> usable by anyone else.  ( I will talk to Steve Millard about adding tau
> with multiple censoring limits to EnvStats, because we are writing a 2nd
> edition of the text to go with the R library).
>
> If you want to use imputation (what you are doing by simulating values for
> the censored observations), you need to use multiple imputation (i.e.,
> generating more than one simulated data set).   I didn't look at your code
> carefully enough to tell if it currently does multiple imputation.  Rubin's
> books (or web links to multiple imputation) will show you how to combine
> results from the multiple imputations.  If you only simulate one data set,
> your conclusions are about that specific simulated data set, not a
> Monte-Carlo approximation to conclusions from the data at hand with
> censoring.
>
> Best wishes,
> Philip
>
>
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