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Title: Targeted weight estimation in the heteroscedastic partially linear model Authors:  Elliot Young - University of Cambridge (United Kingdom) [presenting]
Rajen D Shah - University of Cambridge (United Kingdom)
Abstract: Heteroscedasticity is common in many regression settings, a prime example being (partially) linear mixed effects models. In order to estimate regression coefficients in such models accurately, we must account for this via weighted estimation. Classical approaches use weights derived from parametric models for the conditional covariance function (CCF). We show, however, that in the inevitable case where these models are misspecified, both (restricted) maximum likelihood and regressing squared residuals onto covariates to estimate the CCF can lead to poor estimation of target parameters that may even be substantially worse than using no weighting at all. Instead, we propose to choose weights to directly minimise an estimate of the asymptotic variance of the parameter of interest. When used with a potentially misspecified model for the weights, we argue that in contrast to classical approaches, this always yields an asymptotically optimal estimate of the target parameter subject to the modelling constraints imposed. We introduce a computationally efficient boosting scheme to perform this optimisation that can leverage flexible machine learning methods to approximate the unknown CCF. We demonstrate the effectiveness of our approach on real and simulated data.