Replicate histograms

The ''replicate histogram'' is introduced as a simple diagnostic tool for describing the sampling distribution of a general statistic. It can be applied to virtually any statistic that has an asymptotic distribution. and the data on which the statistic is computed may be serially or spatially dependent. The method is completely sample based, requiring no theoretical analysis by the user, no knowledge of the proper standardization for the statistic, and no specification of the underlying dependence mechanism generating the data. The replicate histogram warns the user of nonnormal sampling distributions and also indicates the type of departure from normality (e.g., skewness, peakedness). in the case of spatially dependent data, the statistic may be computed on observations from irregularly shaped index sets, Large-sample validity of the replicate histogram is established via strong consistency results, which art proved under mild conditions for bath the rime series and random field cases. Numerical examples are presented illustrating the diagnostic power of the replicate histogram for time series and spatial data sets. The bias, variance, and mean squared error performance of the replicate histogram are analyzed via second-order theory.