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• W2034106324 abstract "Let $(X, Y)$ be an $mathbb{R}^d times mathbb{R}$-valued random vector and let $(X_1, Y_1), cdots, (X_n, Y_n)$ be a random sample drawn from its distribution. We study the consistency properties of the kernel estimate $m_n(x)$ of the regression function $m(x) = E{Ymid X = x}$ that is defined by $m_n(x) = Sigma^n_{i=1} Y_ik((X_i - x)/h_n)/Sigma^n_{i=1}k((X_i - x)/h_n)$ where $k$ is a bounded nonnegative function on $mathbb{R}^d$ with compact support and ${h_n}$ is a sequence of positive numbers satisfying $h_n rightarrow_n0, nh^d_n rightarrow_ninfty$. It is shown that $E{int|m_n(x) - m(x)|^pmu(dx)} rightarrow_n 0$ whenever $E{|Y|^p} < infty(p geqslant 1)$. No other restrictions are placed on the distribution of $(X, Y)$. The result is applied to verify the Bayes risk consistency of the corresponding discrimination rules." @default.
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• W2034106324 date "1980-03-01" @default.
• W2034106324 modified "2023-10-17" @default.
• W2034106324 title "Distribution-Free Consistency Results in Nonparametric Discrimination and Regression Function Estimation" @default.
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• W2034106324 doi "https://doi.org/10.1214/aos/1176344949" @default.
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