AN ASYMPTOTIC THEORY FOR WEIGHTED LEAST-SQUARES WITH WEIGHTS ESTIMATED BY REPLICATION Academic Article

abstract

• We consider a heteroscedastic linear regression model with replication. To estimate the variances, one can use the sample variances or the sample average squared errors from a regression fit. We study the large-sample properties of these weighted least-squares estimates with estimated weights when the number of replicates is small. The estimates are generally inconsistent for asymmetrically distributed data. If sample variances are used based on m replicates, the weighted least-squares estimates are inconsistent for m = 2 replicates even when the data are normally distributed. With between 3 and 5 replicates, the rates of convergence are slower than the usual square root of N. With m 6 replicates, the effect of estimating the weights is to increase variances by (m-5)/(m-3), relative to weighted least-squares estimates with known weights. 1988 Biometrika Trust.

authors

• Carroll, Raymond
• Cline, Daren

published proceedings

• BIOMETRIKA

author list (cited authors)

• CARROLL, R. J., & CLINE, D.

citation count

• 33

complete list of authors

• CARROLL, RJ||CLINE, DBH

publication date

• March 1988

publisher

• Oxford University Press (OUP)  Publisher

published in

• Biometrika  Journal

keywords

• 38 Economics
• 3802 Econometrics
• 49 Mathematical Sciences
• 4905 Statistics

Digital Object Identifier (DOI)

• 10.1093/biomet/75.1.35

start page

• 35

end page

• 43

volume

• 75

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1093%2Fbiomet%2F75.1.35