Reliability of a Variance Estimate Obtained from a Sample Augmented by Multivariate Regression
Gilroy, E. J.
Журнал:
Water Resources Research
Дата:
1970
Аннотация:
A sample of size n<sub>1</sub> of a normal random variable y is augmented by n<sub>2</sub> regression estimates obtained from p other random variables which, along with y, follow a (p + 1) dimensional normal probability law. The sampling variance of s<sub>y</sub><sup>2</sup>, the estimate of the variance of y obtained from the augmented sample, is derived. The relative reliability of s<sub>y</sub><sup>2</sup> and s<sub>y</sub><sup>2</sup> (n<sub>1</sub>), the variance estimate based on the original n<sub>1</sub> observations, is found to depend on n<sub>1</sub>, n<sub>2</sub>, p, and R, the multiple correlation between y and the remaining p variables.
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