Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data

By Michael Kohler, Adam Krzyzak, Harro Walk. 2006

55 citations recorded by the source corpus.

Estimation of regression functions from independent and identically distributed data is considered. The L"2 error with integration with respect to the design measure is used as an error criterion. Usually in the analysis of the rate of convergence of estimates besides smoothness assumptions on the regression function and moment conditions on Y also boundedness assumptions on X are made. In this article we consider partitioning and nearest neighbor estimates and show that by replacing the boundedness assumption on X by a proper moment condition the same rate of convergence can be shown as for bounded data.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/94c6060339f35e6111a459196a2c12cc501bb903

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In Artificial Intelligence

In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators☆ (2013, background): “…in j, we have V̂n/Vn−1 = Tn1+Tn2+Tn3+op(1), where Tn1 = V−1n V̂n −V −1 n Jdn j=1 1n,jΘ ′ j Ω̂ −1 j Γ̃jΩ̂ −1 j Θj/qj, Tn2 = V −1 n Jdn j=1 1n,jΘ ′ j (Ω̂−1j +Ω −1 j )Γ̃j(Ω̂ −1 j −Ω −1 j )Θj/qj, Tn3 = V −1 n Jdn j=1Θ ′ jΩ −1 j (Γ̃j − Γj)Ω −1 j Θj/qj, and Γ̃j = n i=1 R̃j(Xi)R̃j(Xi) ′ε2i /(nqj).”