Financial Risk Manager Part 1

Explanation

In multiple linear regression, when an estimator is described as consistent, it means that:

• The estimates converge to the true population values as the sample size increases
• As we collect more data (larger sample size n), the estimator's output gets progressively closer to the actual parameter values
• This is a large-sample property that doesn't guarantee accuracy at any fixed sample size

Why other options are incorrect:

• A: This describes unbiasedness, not consistency. An unbiased estimator has an expected value equal to the true parameter, but this can occur at any sample size.

• B: Consistency doesn't guarantee closeness "regardless of sample size" - it specifically depends on sample size increasing.

• D: Consistency doesn't automatically imply unbiasedness or efficiency. An estimator can be consistent but biased in finite samples, and efficiency is a separate property related to minimum variance.

Key Takeaway:

Consistency is about asymptotic behavior - as n → ∞, the estimator converges in probability to the true parameter value. This is a fundamental property for reliable statistical inference in large samples.