Motivated by applications to goodness of fit testing, the empirical
likelihood approach is generalized to allow for the number of constraints to
grow with the sample size and for the constraints to use estimated criteria
functions. The latter is needed to deal with nuisance parameters. The proposed
empirical likelihood based goodness of fit tests are asymptotically
distribution free. For univariate observations, tests for a specified
distribution, for a distribution of parametric form, and for a symmetric
distribution are presented. For bivariate observations, tests for independence
are developed.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ440 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Background: Mean-based clustering algorithms such as bisecting k-means generally lack robustness. Although componentwise median is a more robust alternative, it can be a poor center representative for high dimensional data. We need a new algorithm that is robust and works well in high dimensional data sets e.g. gene expression data.
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