Minimax nonparametric prediction

Volume 28 / 2001

Maciej Wilczy/nski Applicationes Mathematicae 28 (2001), 83-92 MSC: 62C20, 62G05. DOI: 10.4064/am28-1-6

Abstract

Let $U_{0}$ be a random vector taking its values in a measurable space and having an unknown distribution $P$ and let $U_{1},\dots,U_{n}$ and $V_{1},\dots,V_{m}$ be independent, simple random samples from $P$ of size $n$ and $m$, respectively. Further, let $z_{1},\dots ,z_{k} $ be real-valued functions defined on the same space. Assuming that only the first sample is observed, we find a minimax predictor ${\boldsymbol d}^{0}(n,U_{1},\dots,U_{n})$ of the vector ${\boldsymbol Y}^{m} = \sum _{j=1}^{m} (z_{1}(V_{j}),\dots ,z_{k}(V_{j}))^{T}$ with respect to a quadratic errors loss function.

Authors

  • Maciej Wilczy/nskiInstitute of Mathematics
    Wroc/law University of Technology
    Wybrze/ze Wyspia/nskiego 27
    50-370 Wroc/law, Poland
    e-mail

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