Does sequential augmenting of simple linear heteroscedastic regression reduce variances of ordinary least-squares estimators?

Andrzej S. Kozek*, Brian Jersky

*Corresponding author for this work

    Research output: Contribution to journalArticle

    Abstract

    If uncorrelated random variables have a common expected value and decreasing variances, then the variance of a sample mean is decreasing with the number of observations. Unfortunately, this natural and desirable variance reduction property (VRP) by augmenting data is not automatically inherited by ordinary least-squares (OLS) estimators of parameters. We derive a new decomposition for updating the covariance matrices of the OLS which implies conditions for the OLS to have the VRP. In particular, in the case of a straight-line regression, we show that the OLS estimators of intercept and slope have the VRP if the values of the explanatory variable are increasing. This also holds true for alternating two-point experimental designs.

    Original languageEnglish
    Pages (from-to)1106-1121
    Number of pages16
    JournalStatistics
    Volume48
    Issue number5
    DOIs
    Publication statusPublished - 1 Sep 2014

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