Geodesic
Estimation of multivariate regression
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 2, pp. 301-320

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Let $(X,Y)$ be a random vector whose first component takes on values in a measurable space $(\mathfrak{X},\mathfrak{A},\mu)$ with measure $\mu$ and $Y$ be a real-valued random variable. Let $$ f(x)=E\{Y\mid X=x\} $$ be the regression function of $Y$ on $X$. We consider the problem of estimating $f(x)$ by observations of $n$ independent copies of $(X,Y)$ given $f\inF$, where $F$ is an a priori known set with specified metric characteristics such as $\varepsilon$-entropy or Kolmogorov widths.
Keywords: additive regression, nonparametric estimation, regression function.
Mots-clés : regression 
@article{TVP_2003_48_2_a4,
     author = {I. A. Ibragimov},
     title = {Estimation of multivariate regression},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {301--320},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_2_a4/}
}
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I. A. Ibragimov. Estimation of multivariate regression. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 2, pp. 301-320. http://geodesic.mathdoc.fr/item/TVP_2003_48_2_a4/