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- W4297789654 abstract "Regression models, in which the observed features $X in R^p$ and the response $Y in R$ depend, jointly, on a lower dimensional, unobserved, latent vector $Z in R^K$, with $K< p$, are popular in a large array of applications, and mainly used for predicting a response from correlated features. In contrast, methodology and theory for inference on the regression coefficient $beta$ relating $Y$ to $Z$ are scarce, since typically the un-observable factor $Z$ is hard to interpret. Furthermore, the determination of the asymptotic variance of an estimator of $beta$ is a long-standing problem, with solutions known only in a few particular cases. To address some of these outstanding questions, we develop inferential tools for $beta$ in a class of factor regression models in which the observed features are signed mixtures of the latent factors. The model specifications are practically desirable, in a large array of applications, render interpretability to the components of $Z$, and are sufficient for parameter identifiability. Without assuming that the number of latent factors $K$ or the structure of the mixture is known in advance, we construct computationally efficient estimators of $beta$, along with estimators of other important model parameters. We benchmark the rate of convergence of $beta$ by first establishing its $ell_2$-norm minimax lower bound, and show that our proposed estimator is minimax-rate adaptive. Our main contribution is the provision of a unified analysis of the component-wise Gaussian asymptotic distribution of $wh beta$ and, especially, the derivation of a closed form expression of its asymptotic variance, together with consistent variance estimators. The resulting inferential tools can be used when both $K$ and $p$ are independent of the sample size $n$, and when both, or either, $p$ and $K$ vary with $n$, while allowing for $p > n$." @default.
- W4297789654 created "2022-10-01" @default.
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- W4297789654 date "2019-05-29" @default.
- W4297789654 modified "2023-09-30" @default.
- W4297789654 title "Inference in latent factor regression with clusterable features" @default.
- W4297789654 doi "https://doi.org/10.48550/arxiv.1905.12696" @default.
- W4297789654 hasPublicationYear "2019" @default.
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