CONTINUITY OF SCALE PARAMETER ESTIMATORS WITH RESPECT
TO STOCHASTIC ORDERS
Jarosław Bartoszewicz
Magdalena Frąszczak
Abstract: Lehmann and Rojo [8] proposed a concept of invariance of stochastic orders and
related probability metrics with respect to increasing transformations of random variables.
Bartoszewicz and Benduch [3] and Bartoszewicz and Frąszczak [4] applied a concept of
Lehmann and Rojo to new settings. In the paper these results are applied to the problem of
robustness in the sense of Zieliński [11], [12]. Metrics related to some stochastic orders are
used to study the continuity (robustness) of scale parameter estimators when contaminations
of the models are generated by stochastic orders. The exponential model is considered in
detail.
2000 AMS Mathematics Subject Classification: 62F10, 62F35, 60E05, 60E15,
62N05.
Keywords and phrases: Life distributions, partial orders, order statistics, probability
metrics, robustness.