Publication Date:
2019-07-13
Description:
When it is known a priori exactly to which finite dimensional manifold the probability density function gives rise to a set of samples, the parametric maximum likelihood estimation procedure leads to poor estimates and is unstable; while the nonparametric maximum likelihood procedure is undefined. A very general theory of maximum penalized likelihood estimation which should avoid many of these difficulties is presented. It is demonstrated that each reproducing kernel Hilbert space leads, in a very natural way, to a maximum penalized likelihood estimator and that a well-known class of reproducing kernel Hilbert spaces gives polynomial splines as the nonparametric maximum penalized likelihood estimates.
Keywords:
STATISTICS AND PROBABILITY
Type:
NASA-CR-144384
,
REPT-275-025-016
,
Ann. Meeting of the Inst. of Mathematical Statistics; Aug 15, 1974; Edmonton; Canada
Format:
application/pdf
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