Modeling probability density through ultraspherical polynomial transformations
Mäkinen, Terhi; Holmström, Lasse (2016-05-27)
Terhi Mäkinen & Lasse Holmström (2017) Modeling probability density through ultraspherical polynomial transformations, Communications in Statistics - Simulation and Computation, 46:8, 5879-5900, DOI: 10.1080/03610918.2016.1186181
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in statistics: simulation and computation on 27 May 2016, available online: http://www.tandfonline.com/10.1080/03610918.2016.1186181.
We present a method for fitting parametric probability density models using an integrated square error criterion on a continuum of weighted Lebesgue spaces formed by ultraspherical polynomials. This approach is inherently suitable for creating mixture model representations of complex distributions and allows fully autonomous cluster analysis of high-dimensional datasets. The method is also suitable for extremely large sets, allowing post facto model selection and analysis even in the absence of the original data. Furthermore, the fitting procedure only requires the parametric model to be pointwise evaluable, making it trivial to fit user-defined models through a generic algorithm.
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