Abstract
As an approximation to the regression function $m$ of $Y$ on $X$ based upon empirical data, E. A. Nadaraya and G. S. Watson have studied estimates of $m$ of the form $m_n(x) = \sum Y_ik((x - X_i)/a_n)/\sum k((x - X_i)/a_n)$. For distinct points $x_1, \cdots, x_k$, we establish conditions under which $(na_n)^{\frac{1}{2}}(m_n(x_1) - m(x_1), \cdots, m_n(x_k) - m(x_k))$ is asymptotically multivariate normal.
Citation
Eugene F. Schuster. "Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points." Ann. Math. Statist. 43 (1) 84 - 88, February, 1972. https://doi.org/10.1214/aoms/1177692703
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