2010/05/31 by Peter Ruckdeschel, Ruckdeschel, Peter
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1006.0045
openalex publication_date 2010/05/31 · arxiv created 2010/06/01 · arxiv updated 2010/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide an asymptotic expansion of the maximal mean squared error (MSE) of the sample median to be attained on shrinking gross error neighborhoods about an ideal central distribution. More specifically, this expansion comes in powers of n-1/2, for n the sample size, and uses a shrinking rate of n-1/2 as well. This refines corresponding results of first order asymptotics to be found in Rieder[94]. In contrast to usual higher order asymptotics, we do not approximate distribution functions (or densities) in the first place, but rather expand the risk directly. Our results are illustrated by comparing them to the results of a simulation study and to numerically evaluated exact MSE's in both ideal and contaminated situation.