Mode testing via higher-order density estimation

We investigate the use of fourth-order (reduced bias) variants on kernel density estimation in Silverman’s (J Roy Stat Soc B 43:97–99, 1981) critical bandwidth test of multimodality. Simulations suggest that variable-bandwidth estimates in the style of Abramson (Ann Stat 10:1217–1223, 1982) appear to be especially favorable to mode testing. Conversely, the use of fourth-order kernels leads to extremely poor properties and should be strongly discouraged.