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- W2105803486 abstract "Let $Theta$ be a convex subset of $R^d$, and for each $theta in Theta$ let $F(theta; dt)$ be a probability on the line. For any vector $a_n = (a_{n1}, a_{n2}, cdots, a_{nn})$ where $a_{ni} in Theta$, let $X_{n1}, cdots, X_{nn}$ be independent observations, the distribution of $X_{ni}$ being $F(a_{ni}; dt)$. The main results give a method of estimating the unknown regression function $a_n$ based on a minimum distance recipe. Under regularity assumptions, the proposed estimators are shown, in an appropriate framework, to be asymptotically normal, locally asymptotically minimax, and robust. The abstract results are illustrated by application to the linear model and to exponential response models. In general, nothing at all is assumed about the form of the regression function; accordingly, this forces the limiting normal distributions of the proposed estimators to be located on infinite dimensional linear spaces." @default.
- W2105803486 created "2016-06-24" @default.
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- W2105803486 date "1982-09-01" @default.
- W2105803486 modified "2023-09-25" @default.
- W2105803486 title "Optimal Estimation of a General Regression Function" @default.
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- W2105803486 doi "https://doi.org/10.1214/aos/1176345867" @default.
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