Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects
Keyword(s):
We consider a rather general problem of nonparametric estimation of an uncountable set of probability density functions (p.d.f.’s) of the form: f ( x ; r ) , where r is a non-random real variable and ranges from R 1 to R 2 . We put emphasis on the algorithmic aspects of this problem, since they are crucial for exploratory analysis of big data that are needed for the estimation. A specialized learning algorithm, based on the 2D FFT, is proposed and tested on observations that allow for estimate p.d.f.’s of a jet engine temperatures as a function of its rotation speed. We also derive theoretical results concerning the convergence of the estimation procedure that contains hints on selecting parameters of the estimation algorithm.
2014 ◽
Vol 109
(508)
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pp. 1546-1564
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2006 ◽
Vol 153
(4)
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pp. 462-468
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2021 ◽
Vol 502
(2)
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pp. 1768-1784