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ROBUST_LINEFIT

ROBUST_LINEFIT

Name


      ROBUST_LINEFIT

Purpose


      An outlier-resistant two-variable linear regression.

Explanation


      Either Y on X or, for the case in which there is no true independent
      variable, the bisecting line of Y vs X and X vs Y is calculated. No
      knowledge of the errors of the input points is assumed.

Calling Sequence


      COEFF = ROBUST_LINEFIT( X, Y, YFIT, SIG, COEF_SIG, [ /BISECT,
                      BiSquare_Limit = , Close_factor = , NumIT = ] )

Inputs


      X = Independent variable vector, floating-point or double-precision
      Y = Dependent variable vector

Outputs


      Function result = coefficient vector.
      If = 0.0 (scalar), no fit was possible.
      If vector has more than 2 elements (the last=0) then the fit is dubious.

Optional Output Parameters


      YFIT = Vector of calculated y's
      SIG = The "standard deviation" of the fit's residuals. If BISECTOR
              is set, this will be smaller by ~ sqrt(2).
      COEF_SIG = The estimated standard deviations of the coefficients. If
              BISECTOR is set, however, this becomes the vector of fit
              residuals measured orthogonal to the line.

Optional Input Keywords


      NUMIT = the number of iterations allowed. Default = 25
      BISECT if set, the bisector of the "Y vs X" and "X vs Y" fits is
              determined. The distance PERPENDICULAR to this line is used
              in calculating weights. This is better when the uncertainties
              in X and Y are comparable, so there is no true independent
              variable. Bisquare_Limit Limit used for calculation of
              bisquare weights. In units of outlier-resistant standard
              deviations. Default: 6.
              Smaller limit ==>more resistant, less efficient
  Close_Factor - Factor used to determine when the calculation has converged.
              Convergence if the computed standard deviation changes by less
              than Close_Factor * ( uncertainty of the std dev of a normal
              distribution ). Default: 0.03.

Subroutine Calls


      ROB_CHECKFIT
      ROBUST_SIGMA, to calculate a robust analog to the std. deviation

Procedure


      For the initial estimate, the data is sorted by X and broken into 2
      groups. A line is fitted to the x and y medians of each group.
      Bisquare ("Tukey's Biweight") weights are then calculated, using the
      a limit of 6 outlier-resistant standard deviations.
      This is done iteratively until the standard deviation changes by less
      than CLOSE_ENOUGH = CLOSE_FACTOR * {uncertainty of the standard
              deviation of a normal distribution}

Revision History


      Written, H. Freudenreich, STX, 4/91.
      4/13/93 to return more realistic SS's HF
      2/94 --more error-checking, changed convergence criterion HF
      5/94 --added BISECT option. HF.
      8/94 --added Close_Factor and Bisquare_Limit options Jack Saba.
      4/02 --V5.0 version, use MEDIAN(/EVEN) W. Landsman



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