Financial Risk Manager Part 1

An unbiased estimator is defined as an estimator whose expected value equals the true value of the parameter being estimated. Mathematically, an estimator $\hat{\theta}$ is unbiased for parameter $\theta$ if $E[\hat{\theta}] = \theta$.

Key points:

• Option A describes consistency (an estimator becomes more accurate as sample size increases)
• Option B describes efficiency (minimum variance among unbiased estimators)
• Option C is incorrect as accuracy typically decreases with smaller sample sizes
• Option D correctly defines unbiasedness: the expected value of the estimator equals the parameter value

Example: The sample mean $\bar{x}$ is an unbiased estimator of the population mean $\mu$ because $E[\bar{x}] = \mu$.