Efficient estimation of the mode of continuous multivariate data

Mode estimation is an important task, because it has applications to data from a wide variety of sources. Many mode estimates have been proposed with most based on nonparametric density estimates. However, mode estimates obtained by such methods, although they perform excellently with large sample sizes, perform non-satisfactorily with practical (i.e., small to moderate) sample sizes. Recently, Bickel (2003) proposed an efficient method to estimate the mode of continuous univariate data, and showed that its performance is excellent with small to moderate sample sizes. In this paper, we extend Bickel’s method to continuous multivariate data by using the multivariate Box–Cox transform. The excellent performance of the proposed method at practical sample sizes is demonstrated by simulation examples and two real examples from the fields of climatology and image recognition.