Question

does the "unbiased" aspect of unbiased estimator indicate that it underestimates the population value with same tenency as it overestimates the population value, or not?

Answer 1

That is a good question. So to answer the same, we have to understand why the unbiased estimators are called 'unbiased'.

Whenever we talk about unbiased estimators, that means that the average of the sample statistic over multiple samples will be equal to the population parameter.

We have a large population whose parameter we need to estimate. Now drawing samples from this population, we find out the sample statistic. This statistic may underestimate or overestimate the population parameter. It will be called an unbiased estimator if across multiple samples, the average of this particular sample statistic equals the population parameter.

For example, let us talk about sample variance. If many different samples are selected, the average of the sample variances will be equal to the population variance.

So YES, the "unbiased" aspect of an unbiased estimator indicates that it underestimates the population value with the same tenency as it overestimates the population value.

Please upvote. Let me know in the comments if anything is unclear. I will reply ASAP!