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Reliability of a Variance Estimate Obtained from a Sample Augmented by Multivariate Regression
Author(s) -
Gilroy E. J.
Publication year - 1970
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr006i006p01595
Subject(s) - statistics , mathematics , multivariate statistics , variance (accounting) , regression analysis , sample (material) , multivariate normal distribution , random variable , regression , chemistry , accounting , chromatography , business
A sample of size n 1 of a normal random variable y is augmented by n 2 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 y 2 , the estimate of the variance of y obtained from the augmented sample, is derived. The relative reliability of s y 2 and s y 2 ( n 1 ), the variance estimate based on the original n 1 observations, is found to depend on n 1 , n 2 , p , and R , the multiple correlation between y and the remaining p variables.