In this paper, 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.
Key words: order statistics, permanents, log-concavity, outliers, single-outlier model,
multiple-outlier model, recurrence relations, robust estimators, sensitivity, bias, mean
square error, location-outlier, scale-outlier, censoring, progressive Type-II censoring,
ranked set sampling.
2000 Mathematics Subject Classification: 62E15, 62F10, 62F35, 62G30, 62G35, 62N01.