Minimax nonparametric prediction

Maciej Wilczyński. "Minimax nonparametric prediction." Applicationes Mathematicae 28.1 (2001): 83-92. <http://eudml.org/doc/279717>.

@article{MaciejWilczyński2001,
abstract = {Let U₀ be a random vector taking its values in a measurable space and having an unknown distribution P and let U₁,...,Uₙ and $V₁,...,V_\{m\}$ be independent, simple random samples from P of size n and m, respectively. Further, let $z₁,..., z_\{k\}$ 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 $Y^\{m\} = ∑_\{j=1\}^\{m\} (z₁(V_\{j\}),..., z_\{k\}(V_\{j\}))^\{T\}$ with respect to a quadratic errors loss function.},
author = {Maciej Wilczyński},
journal = {Applicationes Mathematicae},
keywords = {minimax prediction; Dirichlet process; nonparametric prediction},
language = {eng},
number = {1},
pages = {83-92},
title = {Minimax nonparametric prediction},
url = {http://eudml.org/doc/279717},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Maciej Wilczyński
TI - Minimax nonparametric prediction
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 1
SP - 83
EP - 92
AB - Let U₀ be a random vector taking its values in a measurable space and having an unknown distribution P and let U₁,...,Uₙ and $V₁,...,V_{m}$ be independent, simple random samples from P of size n and m, respectively. Further, let $z₁,..., z_{k}$ 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 $Y^{m} = ∑_{j=1}^{m} (z₁(V_{j}),..., z_{k}(V_{j}))^{T}$ with respect to a quadratic errors loss function.
LA - eng
KW - minimax prediction; Dirichlet process; nonparametric prediction
UR - http://eudml.org/doc/279717
ER -