The number of modes
(also known as modality) of a kernel density estimator (KDE) draws lots of
interests and is important in practice. In this paper, we develop an inference
framework on the modality of a KDE under multivariate setting using Gaussian
kernel. We applied the modal clustering method proposed by  for mode hunting. A test statistic and its
asymptotic distribution are derived to assess the significance of each mode.
The inference procedure is applied on both simulated and real data sets.
Tibshirani, R., Walther, G. and Hastie, T. (2001) Estimating the Number of Clusters in a Data Set via the Gap Statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63, 411-423. http://dx.doi.org/10.1111/1467-9868.00293
Fraley, C. and Raftery, A.E. (2002) Model-Based Clustering, Discriminant Analysis, and Density Estimation. Journal of the American Statistical Association, 97, 611-631. http://dx.doi.org/10.1198/016214502760047131
Burman, P. and Polonik, W. (2009) Multivariate Mode Hunting: Data Analytic Tools with Measures of Significance. Journal of Multivariate Analysis, 100, 1198-1218. http://dx.doi.org/10.1016/j.jmva.2008.10.015
Lindsay, B.G., Markatou, M., Ray, S., Yang, K. and Chen, S.C. (2008) Quadratic Distances on Probabilities: A Unified Foundation. The Annals of Statistics, 36, 983-1006. http://dx.doi.org/10.1214/009053607000000956