Strong convergence of the estimated asymptotic variance (σ2(Ta(HN))) of generalized L-statistics is demonstrated for smooth and discrete weighting functions. For smooth weighting functions that are trimmed, such as the 25%-trimmed mean, and for discrete functions, such as the median, minimal conditions are required for strong convergence of σ2(Ta(HN)). In a simulation study, σ2(Ta(HN)) for the trimmed mean, but not the median, appeared to converge to the sample variance of the statistic for samples from three distributions (normal, contaminated normal and Cauchy). For the smallest sample in the study (n = 16), σ2(Ta(HN)) tended to underestimate the sample variance of the GL-statistics.
All Science Journal Classification (ASJC) codes
- Statistics and Probability