Minimax nonparametric prediction

Maciej Wilczyński

Applicationes Mathematicae, Tome 28 (2001), p. 83-92 / Harvested from The Polish Digital Mathematics Library

Résumé

Let U₀ be a random vector taking its values in a measurable space and having an unknown distribution P and let U₁,...,Uₙ and $V ₁, . . ., V_{m}$ be independent, simple random samples from P of size n and m, respectively. Further, let $z ₁, . . ., z_{k}$ be real-valued functions defined on the same space. Assuming that only the first sample is observed, we find a minimax predictor d⁰(n,U₁,...,Uₙ) of the vector $Y^{m} = \sum_{j = 1}^{m} {(z ₁ (V_{j}), . . ., z_{k} (V_{j}))}^{T}$ with respect to a quadratic errors loss function.

Publié le : 2001-01-01

Zbl 1008.62512

EUDML-ID : urn:eudml:doc:279717

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     author = {Maciej Wilczy\'nski},
     title = {Minimax nonparametric prediction},
     journal = {Applicationes Mathematicae},
     volume = {28},
     year = {2001},
     pages = {83-92},
     zbl = {1008.62512},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-6}
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Maciej Wilczyński. Minimax nonparametric prediction. Applicationes Mathematicae, Tome 28 (2001) pp. 83-92. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-6/