The connection between regularization and min–max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min–max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.

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Spatial dynamic microsimulations allow for the multivariate analysis of complex socioeconomic systems with geographic segmentation. For this, a synthetic replica of the system as base population is stochastically projected into future periods. Thereby, the projection is based on micro-level transition probabilities. They need to accurately represent the characteristic dynamics of the system to allow for reliable simulation outcomes. In practice, transition probabilities are unknown and must be estimated from suitable survey data. This can be challenging when the characteristic dynamics vary locally. Survey data often lacks in regional detail due to confidentiality restrictions and limited sampling resources. In that case, transition probability estimates may misrepresent local dynamics as a result of insufficient local observations and coverage problems. The simulation process then fails to provide an authentic evolution. We present two transition probability estimation techniques that account for regional heterogeneity when the survey data lacks in regional detail. Using methods of constrained optimization and ex-post alignment, we show that local micro level transition dynamics can be accurately recovered from aggregated regional benchmarks. The techniques are compared in theory and subsequently tested in a simulation study.

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