Question

What exactly is a unbiased estimatior? This is more of a contextual question for understanding.

Answer 1

A parameter is a single measure of some attribute of a population, which is, most of the times, unknown to us. A statistic is a single measure of some attribute of a sample (sample drawn from the population stated above), which is known to us. A statistic is used to estimate the value of the parameter.

Also, by definition, a sampling distribution is a probability distribution of a statistic which is obtained through a large number of samples drawn from a specific population.

Now, we call a statistic to be an unbiased estimator of a given parameter when the mean (or expected value) of the sampling distribution of that statistic can be shown to be equal to the parameter being estimated.

The best example - the mean of a sample is an unbiased estimate of the mean of the population from which the sample was drawn.

We write it as :