For estimating a population characteristic, why is an...

Name: Problem 7, Chapter 9: Statistics Learning From Data
Uploaded: 2020-07-09T15:03:33-08:00
Duration: 1 min 22 s
Channel: Sara Sasani
Description: For estimating a population characteristic, why is an unbiased statistic generally preferred over a biased statistic? Does unbiasedness alone guarantee that the estimate will be close to the actual value of the population characteristic? Explain.

For estimating a population characteristic, why is an unbiased statistic generally preferred over a biased statistic? Does unbiasedness alone guarantee that the estimate will be close to the actual value of the population characteristic? Explain.

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Key Concepts

Unbiased Estimator

An unbiased estimator is a statistic whose expected value equals the true population parameter. This means that on average, across repeated samples, the estimator neither systematically overestimates nor underestimates the parameter. This property is desirable because it ensures that the estimation process does not introduce systematic error.

Variance and Mean Squared Error

Even though an estimator may be unbiased, its estimates in individual samples can vary widely if the variance is high. The mean squared error (MSE), which combines both bias and variance, is a more comprehensive measure of estimator accuracy. Therefore, an estimator with a small bias but a much lower variance could be preferable over an unbiased estimator with high variability, as it may produce estimates that are on average closer to the true parameter.

Bias-Variance Trade-off

The bias-variance trade-off highlights that minimizing bias does not automatically ensure an estimator’s values are close to the true parameter in any given sample. Instead, a balance must be struck where both bias and variance are considered. In some cases, accepting a small bias can lead to significantly reduced variance, thereby improving overall estimation performance as measured by the MSE.

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