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I have used regression to estimate, now I want to calculate the bias in order to compare regression method versus other methods. Could anyone help me? for instance, I have V = 0.06*F + 0.01 based on observed value for "V", I have an estimation for F, but I could not calculate the bias.

parisa
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    To calculate bias you need to know the *true* process that you are estimating. Unless you are working with data you simulated yourself, this is never the case. In general, the bias is a conceptual tool, not a statistic you can compute and report. – Matthew Drury Aug 22 '16 at 16:35
  • Actually I have a real data set, I have bunch of data like: (F1,V1),(F2,V2),...(Fn,Vn), I fit a regression line to them, then I used that line to estimate the unknown F for observed V. now , I need to calculate bias to compare regression method with another method – parisa Aug 22 '16 at 16:48

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Bias is the difference between the value of the (population) parameter and the expected value of the estimate of that parameter. As @matthew-drury points out, unless one knows the population, we cannot calculate the bias. Unless your data is from a complete census of the population or from simulation (when the data is simulated, one sets the parameter for the simulation), the parameters will not be known. Expected value of the estimator itself will require some understanding of the sampling distribution of the estimator and the associated parameters.

Having said that, you can estimate the bias possibly via a bootstrap approach. See for example: When is the bootstrap estimate of bias valid?

Community
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Just_to_Answer
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  • So is the idea that you just try to minimize the MSE though you'll never know how it breaks down into variance and bias^2? – Jon Apr 04 '21 at 02:59