medium · Quantitative Finance prob-stats
An estimator is said to be 'consistent' if it converges in probability to the true parameter value as the sample size grows.
Is the OLS estimator consistent?
- Yes, under standard assumptions such as E[ε] = 0 and no correlation between x and ε.
- Only if the error terms are homoscedastic.
- No, because the random noise ε prevents the estimate from ever reaching the true value.
- Only if the R² of the regression is equal to 1.0.
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