Asymptotic evaluation of weighted nonparametric combination procedures

The asymptotic optimality of four commonly used weighted nonparametric combination procedures is evaluated by applying Bahadur's asymptotic relative efficiency, which is a useful criterion in assessing asymptotic optimal properties of combination procedures. The procedures considered are Fisher's weighted procedure, the weighted logit procedure, the weighted inverse normal procedure and Lancaster's procedure. A Monte-Carlo power simulation is used to evaluate these procedures. The optimal properties of these weighted procedures are discussed according to Badahur's asymptotic relative efficiency and the results of power comparisons. It is shown that although Bahadur's efficiency is an asymptotic criterion to evaluate the procedures's optimality, the conventionally relative performances of these procedures for finite sample sizes present somewhat different features.