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VarianceEstimatorFunction—Wolfram Language Documentation

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BUILT-IN SYMBOL

VarianceEstimatorFunction Details

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 res={y₁-,y₂-,…} 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 is the weight for the ^th data point, is the ^th residual, is the number of data elements, and is the number of parameters in the model.
With VarianceEstimatorFunction->(1&) and Weights->{1/Δy₁²,1/Δy₂²,…}, Δy_i is treated as the known uncertainty of measurement y_i and parameter standard errors are effectively computed only from the weights. »

Examplesopen allclose 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:

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:

Wolfram Research (2008), VarianceEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/VarianceEstimatorFunction.html. Text Wolfram Research (2008), VarianceEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/VarianceEstimatorFunction.html.CMS Wolfram Language. 2008. "VarianceEstimatorFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VarianceEstimatorFunction.html.APA Wolfram Language. (2008). VarianceEstimatorFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VarianceEstimatorFunction.htmlBibTeX @misc{reference.wolfram_2025_varianceestimatorfunction, author="Wolfram Research", title="{VarianceEstimatorFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/VarianceEstimatorFunction.html}", note=[Accessed: 11-July-2025 ]}BibLaTeX @online{reference.wolfram_2025_varianceestimatorfunction, organization={Wolfram Research}, title={VarianceEstimatorFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/VarianceEstimatorFunction.html}, note=[Accessed: 11-July-2025 ]}

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