Which description best matches a statistic with no systematic bias in its expectation?

Which description best matches a statistic with no systematic bias in its expectation?

• A. Unbiased Statistic
• B. Biased Statistic
• C. Efficient Statistic
• D. Consistent Statistic

Answer: (A)

Unbiasedness means the expected value of the statistic equals the true parameter. If you could repeat the sampling many times and compute the statistic each time, the average of those results would converge to the parameter. In other words, there is no systematic bias in how the statistic estimates the parameter on average. A classic example is the sample mean estimating the population mean; its average over repeated samples equals the true mean, so it’s unbiased. Biased statistics have E[T] not equal to the parameter, so they tend to miss the true value on average. Efficient statistics concern having the smallest variability among unbiased estimators, not about bias itself. Consistent statistics converge to the parameter as sample size grows, which can happen with biased estimators as well, though their bias must vanish in the limit for consistency.

Unbiasedness means the expected value of the statistic equals the true parameter. If you could repeat the sampling many times and compute the statistic each time, the average of those results would converge to the parameter. In other words, there is no systematic bias in how the statistic estimates the parameter on average.

A classic example is the sample mean estimating the population mean; its average over repeated samples equals the true mean, so it’s unbiased.

Biased statistics have E[T] not equal to the parameter, so they tend to miss the true value on average. Efficient statistics concern having the smallest variability among unbiased estimators, not about bias itself. Consistent statistics converge to the parameter as sample size grows, which can happen with biased estimators as well, though their bias must vanish in the limit for consistency.