Variance Function Estimation
TL;DR: In this article, the variance function estimation in heteroscedastic regression models is studied in a unified way, focusing on common methods proposed in the statistical and other literature, to make both general observations and compare different estimation schemes.
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Abstract: Heteroscedastic regression models are used in fields including economics, engineering, and the biological and physical sciences. Often, the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters. Standard asymptotic theory implies that how one estimates the variance function, in particular the structural parameters, has no effect on the first-order properties of the regression parameter estimates; there is evidence, however, both in practice and higher-order theory to suggest that how one estimates the variance function does matter. Further, in some settings, estimation of the variance function is of independent interest or plays an important role in estimation of other quantities. In this article, we study variance function estimation in a unified way, focusing on common methods proposed in the statistical and other literature, to make both general observations and compare different estimation schemes. We show that there are significant di...
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