- The linear regression estimator (specifically the ordinary least squares estimator) has the smallest variance among all linear unbiased estimators — this is the Gauss–Markov theorem. It is not the smallest variance among all unbiased estimators in general (nonlinear unbiased estimators could have smaller variance), so the statement is sometimes true but not universally.
- AdaBoost assigns weights (coefficients) to classifiers, and in the original algorithm the weights are derived from the logit of the error; they are non-negative in standard implementations, but some variants or theoretical interpretations allow negative values, so the statement “always non-negative” is sometimes false.
This matches: The first statement is sometimes true, False → option A.
\boxed{A}
