Abstract
Estimation of parameter vector for a linear model with errors-in-variables is considered when the number of regressors may exceed the sample size. As the classical approaches fail in this high-dimensional setting, new approaches are assessed. In particular, we address the problem from two perspectives. Assuming the usual functional model setting, the first solution concerns a generalization of the classical total least squares estimator. The second option assumes structural model and is based on estimating the unknown covariance matrix of large dimension. In both cases, only the exact solutions are considered so that no asymptotics are required. We assume normality, along with a few other mild assumptions, but do not assume any sparsity or related conditions.
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Zwanzig, S., Ahmad, R. (2020). On Parameter Estimation for High Dimensional Errors-in-Variables Models. In: Maciak, M., Pešta, M., Schindler, M. (eds) Analytical Methods in Statistics. AMISTAT 2019. Springer Proceedings in Mathematics & Statistics, vol 329. Springer, Cham. https://doi.org/10.1007/978-3-030-48814-7_8
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