Zapraszamy na trzynaste posiedzenie Seminarium ze Statystyki w czwartek 13 listopada o godz. 12:15 do sali 711, na którym Dr Jeffrey Näf z Research Institute for Statistics and Information Science Uniwersytetu w Genewie wygłosi odczyt pt.
Parametric Maximum Mean Discrepancy Estimation with Missing Values:
Robustness to Missingness and Data Model Misspecification.
Streszczenie:
In the missing data literature, the Maximum Likelihood Estimator (MLE) is celebrated for its ignorability property under missing at random (MAR) data. However, its sensitivity to misspecification of the (complete) data model, even under MAR, remains a significant limitation. This issue is further exacerbated by the fact that the MAR assumption may not always be realistic, introducing an additional source of potential misspecification through the missingness mechanism. In this talk, we propose a novel M-estimation procedure based on the Maximum Mean Discrepancy (MMD), which is provably robust to both model misspecification and deviations from the assumed missingness mechanism. Our approach offers strong theoretical guarantees and improved reliability in complex settings. We establish the consistency and asymptotic normality of the estimator under missingness completely at random (MCAR), provide an efficient stochastic gradient descent algorithm, and derive error bounds that explicitly separate the contributions of model misspecification and missingness bias. Furthermore, we analyze missing not at random (MNAR) scenarios where our estimator maintains controlled error, including a Huber setting where both the missingness mechanism and the data model are contaminated.