Nonlinear Principal Components of univariate symmetric unimodal distributions are considered focusing on the regularity and concavity properties of the first NLPC transformation. This allows to extend a characterization result by Purkayastha and Bhandari of uniform distributions obtained via the Chernoff inequality, and to prove a comparison result on the variances of the first NLPCs.
Explicit computation and estimation of NLPCs transformations for a family of unimodal densities is performed. A goodness-of-fit test for the Wigner distribution is introduced and developed.
Key Words: symmetric unimodal distributions, nonlinear principal components, concavity, Wigner distribution, Chernoff inequality.
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