The Communicability of Graphical Alternatives to Tabular Displays of Statistical Simulation Studies

Simulation studies are often used to assess the frequency properties and optimality of statistical methods. They are typically reported in tables, which may contain hundreds of figures to be contrasted over multiple dimensions. To assess the degree to which these tables are fit for purpose, we performed a randomised cross-over experiment in which statisticians were asked to extract information from (i) such a table sourced from the literature and (ii) a graphical adaptation designed by the authors, and were timed and assessed for accuracy. We developed hierarchical models accounting for differences between individuals of different experience levels (under- and post-graduate), within experience levels, and between different table-graph pairs. In our experiment, information could be extracted quicker and, for less experienced participants, more accurately from graphical presentations than tabular displays. We also performed a literature review to assess the prevalence of hard-to-interpret design features in tables of simulation studies in three popular statistics journals, finding that many are presented innumerately. We recommend simulation studies be presented in graphical form

Iterated bootstrap-t confidence intervals for density functions

Conventional bootstrap-t intervals for density functions based on kernel density estimators exhibit poor coverages due to failure of the bootstrap to estimate the bias correctly. The problem can be resolved by either estimating the bias explicitly or undersmoothing the kernel density estimate to undermine its bias asymptotically. The resulting bias-corrected intervals have an optimal coverage error of order arbitrarily close to second order for a sufficiently smooth density function. We investigated the effects on coverage error of both bias-corrected intervals when the nominal coverage level is calibrated by the iterated bootstrap. In either case, an asymptotic reduction of coverage error is possible provided that the bias terms are handled using an extra round of smoothed bootstrapping. Under appropriate smoothness conditions, the optimal coverage error of the iterated bootstrap-t intervals has order arbitrarily close to third order. Examples of both simulated and real data are reported to illustrate the iterated bootstrap procedures. © 2007 Board of the Foundation of the Scandinavian Journal of Statistics.link_to_subscribed_fulltex

Bootstrap variance estimation for Nadaraya quantile estimator

Nadaraya quantile estimator, Order-calibration, Smoothed bootstrap, 62G05, 62G09, 62G30,