Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points
Schuster, Eugene F.
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 84-88 / Harvested from Project Euclid
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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.
Publié le : 1972-02-14
Classification:  
@article{1177692703,
     author = {Schuster, Eugene F.},
     title = {Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 84-88},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692703}
}

Schuster, Eugene F. Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  84-88. http://gdmltest.u-ga.fr/item/1177692703/