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- W3204346704 abstract "Abstract We study linear subset regression in the context of the high-dimensional overall model $y = vartheta +theta ' z + epsilon $ with univariate response y and a d -vector of random regressors z , independent of $epsilon $ . Here, “high-dimensional” means that the number d of available explanatory variables is much larger than the number n of observations. We consider simple linear submodels where y is regressed on a set of p regressors given by $x = M'z$ , for some $d times p$ matrix M of full rank $p < n$ . The corresponding simple model, that is, $y=alpha +beta ' x + e$ , is usually justified by imposing appropriate restrictions on the unknown parameter $theta $ in the overall model; otherwise, this simple model can be grossly misspecified in the sense that relevant variables may have been omitted. In this paper, we establish asymptotic validity of the standard F -test on the surrogate parameter $beta $ , in an appropriate sense, even when the simple model is misspecified, that is, without any restrictions on $theta $ whatsoever and without assuming Gaussian data." @default.
- W3204346704 created "2021-10-11" @default.
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- W3204346704 date "2021-09-27" @default.
- W3204346704 modified "2023-09-25" @default.
- W3204346704 title "STATISTICAL INFERENCE WITH F-STATISTICS WHEN FITTING SIMPLE MODELS TO HIGH-DIMENSIONAL DATA" @default.
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- W3204346704 doi "https://doi.org/10.1017/s026646662100044x" @default.
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