INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 32
Fora sample of n observations,
, ...,
, the sample variance will be defined as the average squared
deviation in the sample ( )
∑
(
̅)
…[2.22]
The
sample variance,
thus defined, is a biased estimator of the population variance. The reason for the underestimation is because it is calculated as the average squared deviation from the sample mean rather than the true mean. This is because the sample mean is automatically
in the centre of the sample, the deviations from it will tend to be smaller than those from the population mean. Therefore, sample variance as an unbiased estimate of population
variance is given as ∑
(
̅ )
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