Sample Question #195 (statistics – regressions)
How does the weighted least squares (WLS) regression method work? What’s its biggest empirical drawback?
WLS uses a "weight matrix" to derive a consistent least squares estimator; WLS can be seen as a specific example of the GLS method. The weights are meant to "correct" certain problems in the data, such as non-spheric errors. Usually, WLS is carried out by using the inverses of the moment variances as the weights.
The biggest problem can be seen as follows: when the variance of a moment is very small, its inverse will be large. If this happens due to some data measurement error, we inadvertently let this measurement error dominate the WLS estimation. This is a serious defect that every researcher must be aware of.
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