A heteroscedastic linear regression model is considered where responses are allowed to be missing at random. An estimator is constructed that matches the performance of the weighted least squares estimator without the knowledge of the conditional variance function. This is usually done by constructing an estimator of the variance function. Our estimator is a maximum empirical likelihood estimator based on an increasing number of estimated constraints and avoids estimating the variance function.
"Weighted least squares estimation with missing responses: An empirical likelihood approach." Electron. J. Statist. 7 932 - 945, 2013. https://doi.org/10.1214/13-EJS793