Minimax nonparametric prediction

Maciej Wilczy/nski¹

¹ Institute of Mathematics Wroc/law University of Technology Wybrze/ze Wyspia/nskiego 27 50-370 Wroc/law, Poland

Applicationes Mathematicae, Tome 28 (2001) no. 1, pp. 83-92

Résumé

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.

Détail

DOI : 10.4064/am28-1-6

Keywords: random vector taking its values measurable space having unknown distribution dots dots independent simple random samples size respectively further dots real valued functions defined space assuming only first sample observed minimax predictor boldsymbol dots vector boldsymbol sum dots respect quadratic errors loss function