Nonparametric estimation of distributions using orthogonal expansions Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/k0698b00w

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  • Methods of approximation and estimation of the density and the cumulative distribution function of a distribution over a finite interval are investigated. Goodness of the methods is measured pointwise and in terms of mean integrated squared error (MISE). If the density obeys certain regulatory conditions, i. e. , continuous, positive, piecewise smooth, then the canonical exponential family of distributions serve very satisfactorily as an approximation to the true distribution. The theory has wide application to real world problems since the assumptions made are very general. The class of matrix estimators of the density is introduced and is shown to be superior to the usual orthogonal series estimator when comparison is in terms of MISE. Large sample equivalence of the two methods is established.
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