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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 2, Pages 301–320 (Mi tvp286)  

This article is cited in 4 scientific papers (total in 4 papers)

Estimation of multivariate regression

I. A. Ibragimov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: 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, regression function.

DOI: https://doi.org/10.4213/tvp286

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English version:
Theory of Probability and its Applications, 2004, 48:2, 256–272

Bibliographic databases:

Received: 15.11.2002

Citation: I. A. Ibragimov, “Estimation of multivariate regression”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 301–320; Theory Probab. Appl., 48:2 (2004), 256–272

Citation in format AMSBIB
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\yr 2004
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Goldenshluger A., Lepski O., “Structural adaptation via L–p–norm oracle inequalities”, Probability Theory and Related Fields, 143:1–2 (2009), 41–71  crossref  mathscinet  zmath  isi  scopus
    2. Klemela J., Mammen E., “Empirical Risk Minimization in Inverse Problems”, Annals of Statistics, 38:1 (2010), 482–511  crossref  mathscinet  zmath  isi  scopus
    3. A. L. Bunich, “Sistemy upravleniya s identifikatorom”, UBS, 33 (2011), 35–69  mathnet  elib
    4. A. V. Gol'denshlyuger, O. V. Lepskiǐ, “General procedure for selecting linear estimators”, Theory Probab. Appl., 57:2 (2013), 209–226  mathnet  crossref  crossref  zmath  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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