Permanents, order statistics, outliers, and robustness. (English) Zbl 1148.62031
Summary: We consider order statistics and outlier models, and focus primarily on multiple-outlier models and associated robustness issues. We first synthesise recent developments on order statistics arising from independent and non-identically distributed random variables based primarily on the theory of permanents. We then highlight various applications of these results in evaluating the robustness properties of several linear estimators when multiple outliers are possibly present in the sample.
MSC:
62G30 | Order statistics; empirical distribution functions |
62F35 | Robustness and adaptive procedures (parametric inference) |
62E15 | Exact distribution theory in statistics |
62F10 | Point estimation |
62G35 | Nonparametric robustness |
62N01 | Censored data models |
60E15 | Inequalities; stochastic orderings |