[R] Median of streaming data

Martyn Byng martyn.byng at nag.co.uk
Wed Sep 24 12:29:33 CEST 2014

Something else that might be of interest ...

Zhang Q and Wang W (2007) A fast algorithm for approximate quantiles in high speed data streams Proceedings of the 19th International Conference on Scientific and Statistical Database Management IEEE Computer Society 29

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Martin Maechler
Sent: 24 September 2014 09:17
To: Rolf Turner
Cc: R-help at r-project.org; R-SIG-robust at r-project.org
Subject: Re: [R] Median of streaming data

>>>>> Rolf Turner <r.turner at auckland.ac.nz>
>>>>>     on Wed, 24 Sep 2014 18:43:34 +1200 writes:

    > On 24/09/14 17:31, Mohan Radhakrishnan wrote:
    >> Hi,
    >> I have streaming data(1 TB) that can't fit in memory. Is
    >> there a way for me to find the median of these streaming
    >> integers assuming I can fit only a small part in memory ?
    >> This is about the statistical approach to find the median
    >> of a large number of values when I can inspect only a
    >> part of them due to memory constraints.

    > You cannot, I'm pretty sure, calculate the median
    > recursively.  However there are "approximate" recursive
    > median algorithms which provide an estimate of location
    > that has the same asymptotic properties as the median.

    > See:

    > * U. Holst, Recursive estimators of location.
    > Commun. Statist. Theory Meth., vol. 16, 1987,
    > pp. 2201--2226.

    > and

    > * Murray A. Cameron and T. Rolf Turner, Recursive location
    > and scale estimators, Commun. Statist. Theory Meth.,
    > vol. 22, 1993, pp. 2503--2515.

This is really interesting to me, thank you, Rolf!


1) has your proposal ever been provided in R?
   I'd be happy to add it to the robustX
   (http://cran.ch.r-project.org/web/packages/robustX) or even
   robustbase (http://cran.ch.r-project.org/web/packages/robustbase) package.

2) Would anybody know of more recent research on the subject?
   (I quickly "googled around" and found research more geared
    for the time series situation which is more involved anyway)

   --> Hence CC'ing the experts' list  R-SIG-robust

Martin Maechler,  ETH Zurich

    > cheers,
    > Rolf Turner

    > -- 
    > Rolf Turner Technical Editor ANZJS

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