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3277Re: Kalman Filter

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  • dan_t_rosenbaum
    Feb 25, 2004
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      ******************************************************************
      DeanO wrote:
      1. A Kalman Filter can be used to estimate an offensive ability, a
      defensive ability, and an overall rank at the same time -- something
      that Sagarin does, Massey does, etc. for the BCS. It basically
      estimates how many points an offense should score against some
      defense, then readjusts based on the actual results of the game. It
      does the same for the defense, then defines power by offense minus
      defense or divided by or whatever. (What defines the method as a
      Kalman filter is a certain use of different stats. My guess is that
      none of these guys use a Kalman filter exactly, but they do
      continuously estimate and re-estimate -- they use "filters.")

      I think something more like this was done because of some of the
      things that were reported about WINVAL -- that they get offensive and
      defensive rankings for all players, plus the overall number you have.
      ******************************************************************

      DanR replies:

      I have figured out how I can break out offensive and defensive
      rating separately (and add in pace), so I don't think this is a
      distinguishing feature between what I am doing and what
      Sagarin/Massey is doing. I have hesitated in doing this, because it
      is not completely straightforward how to come up with standard
      errors for these separate offensive and defensive ratings -
      something which I suspect Sagarin and Massery don't worry about
      doing.

      This method of estimating and then "readjusting" is exactly what I
      think filters are most applicable for, i.e. cases where re-
      estimating the model over in its entirety is too time consuming.
      (Those are the examples always mentioned in the Kalman filter
      literature that you pointed me to.)

      However, in this case it only take six seconds to completely re-
      estimate the model from scratch, so there doesn't appear to be a
      need to use a filter whose main advantage relative to OLS is that it
      can get estimates in a fraction of the time it takes OLS.

      ******************************************************************
      DeanO wrote:
      Whether it's most "efficient," (an economist's term) I dunno. I know
      that there are references that describe the Kalman as "the optimal
      linear filter." Basically, my sense is that both regression and
      Kalman Filters use variances to optimize their estimates. The Kalman
      does it assuming one model of interaction between the offense and the
      defense, estimating both the offense and defense. Regression does it
      without the interaction modeled, just viewing the point difference as
      The Result and I don't think it can easily back out estimates of
      offense and defense. There are advantages to both. I personally do
      think that the model of interaction between offense and defense in
      most filters is not right (doesn't adequately account for garbage
      time), but estimating offensive and defensive ability is important.
      ******************************************************************

      DanR replies:

      "Efficiency" is commonly referred to in economics, but I was using
      it in the statistical sense.

      http://www.ruf.rice.edu/~lane/hyperstat/A12977.html

      Yes, I have seen the Kalman filter referred to as an
      optimal "filter," but OLS is not a filter per se, so that is not
      comparing to OLS.

      Now in doing a little more reading, there are times where the Kalman
      Filter may be more efficient than OLS, but these are generally cases
      where we assume that the beta estimates are time-varying or that
      there is some form of serial correlation in the errors. These both
      would be sensible (but hard to implement) assumptions in this case,
      but as far as I can tell, you are not proposing implementing either
      of these assumptions.

      So other than lower computational costs, I cannot see the advantage
      of the Kalman Filter in this application. But I have been wrong
      before, and certainly could be wrong here.

      The OLS model that I use fully accounts for the interaction between
      offense and defense without really specifying a particular
      functional form. And again, I can estimate separate offensive and
      defensive ratings, but I am not sure I can get credible estimates of
      the standard errors for these without resorting to something like
      bootstrapping.
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