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Multivariate mode estimation

1 February 2014

Hsu, Chih-Yuan; Wu, Tiee-Jian
Efficient estimation of the mode of continuous multivariate data. (English summary)
Comput. Statist. Data Anal. 63 (2013), 148–159.
62F10 (62F12)

To estimate the mode of a unimodal multivariate distribution, the authors propose the following algorithm. First, the data are transformed to become approximately multivariate normal by means of a transformation determined by maximum likelihood estimation (MLE) of a transformation parameter joint with the parameters of the multivariate normal distribution. Second, the resulting inverse transformation is applied to the MLE multivariate normal density function, yielding an estimate of the probability density function on the space of the original data. Third, the point at which that density function achieves its maximum is taken as the estimate of the multivariate mode. The paper features a theorem reporting the weak consistency of the estimator under the lognormality of the data.
The authors cite several papers indicating the need for such multivariate mode estimation in applications. They illustrate the practical use of their estimator by applying it to climatology and handwriting data sets.
Simulations indicate a large variety of distributions and dependence structures under which the proposed estimator performs substantially better than its competitors. An exception is the case of contamination with data from a distribution that has a different mode than the mode that is the target of inference.

Reviewed by David R. Bickel

This review first appeared at “Efficient estimation of the mode of continuous multivariate data” (Mathematical Reviews) and is used with permission from the American Mathematical Society.

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