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VarianceEstimatorFunction

VarianceEstimatorFunction
is an option for LinearModelFit and NonlinearModelFit which specifies the variance estimator to use.
  • VarianceEstimatorFunction defines the function for estimating the error variance scale for linear and nonlinear models with assumed normally distributed errors.
  • With the setting VarianceEstimatorFunction->f, the variance scale is estimated by f[res, w] where is the list of residuals and w is the list of weights, as specified by the setting for the Weights option.
  • The default setting Automatic estimates the variance scale by where wi is the weight for the ith data point, is the ith residual, n is the number of data elements and p is the number of parameters in the model.
  • With VarianceEstimatorFunction->(1&) and Weights->{1/CapitalDeltay12, 1/CapitalDeltay22, ...}, CapitalDeltayi is treated as the known uncertainty of measurement yi and parameter standard errors are effectively computed only from the weights.  »
EXAMPLESCLOSE ALL
Basic Examples   (1)
Use the default unbiased estimate of error variance:
Assume a known error variance:
Estimate the variance by the mean squared error:
Use the default unbiased estimate of error variance:
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Assume a known error variance:
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Estimate the variance by the mean squared error:
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Scope   (2)
Define the estimate within the FittedModel:
Use with a nonlinear model:
Estimate the variance by the mean absolute error:
Applications   (1)
Fit a nonlinear model using measurement errors as weights:
Estimate the common error scale by 1:
Obtain standard errors for the parameters:
Compare with estimates using the default variance estimate:
Properties & Relations   (1)
Error estimates and confidence intervals involve variance estimates:
Use the default estimator:
Assume unit error scale:
Estimate by mean squared error:
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