Estimating modes and isopleths

Recent years have witnessed a renewal of interest in estimating the mode and in related multivariate mapping problems. In part, this renaisance may be attributed to the Phillosopoicdi Success of nonparametrics in challenging the dominant (Fisherian) parametric world-view. But the main reason is the recent advent of powerful mathematical tools and computational machinery that render these problems much more tractable. In surveying the mode, this paper has several objectives: (1) to place the development of modal estimation in historical perspective, noting the statistical currents that stimulated and retarded its progress; (2) to present all the methods for estimating the mode that have been studied in the literature; (3) to summarize the mathematical results, including consistency and asymptotic distributions; (4) to evaluate critically the extant simulation studies; (5) to note areas of cross-fertilization with other disciplines and with other areas of statistics, such as density estimation, cartography,...

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