منابع مشابه
Endogeneity in High Dimensions.
Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. A necessary...
متن کاملSupplement to “ Endogeneity in High Dimensions ”
This supplementary material contains the proof of Theorem 7.1 in the main paper. The following lemma is useful. Lemma 0.1. For a general loss function Ln, suppose it is twice differentiable in a neighborhood of β0. Assume max l / ∈S ∣∣∣∣∂Ln(β0) ∂βl ∣∣∣∣ = op(P ′ n(0)), (0.1) and there is a neighborhood U ⊂ R of β0S such that sup βS∈U max l / ∈S,j∈S ∣∣∣∣∂2Ln(βS, 0) ∂βl∂βj ∣∣∣∣ = op(P ′ n(0) skn ...
متن کاملTesting Endogeneity with High Dimensional Covariates∗
Modern, high dimensional data has renewed investigation on instrumental variables (IV) analysis, primary focusing on estimation of the included endogenous variable under sparsity and little attention towards specification tests. This paper studies in high dimensions the Durbin-Wu-Hausman (DWH) test, a popular specification test for endogeneity in IV regression. We show, surprisingly, that the D...
متن کاملTesting Endogeneity with Possibly Invalid Instruments and High Dimensional Covariates
The Durbin-Wu-Hausman (DWH) test is a commonly used test for endogeneity in instrumental variables (IV) regression. Unfortunately, the DWH test depends, among other things, on assuming all the instruments are valid, a rarity in practice. In this paper, we show that the DWH test often has distorted size even if one IV is invalid. Also, the DWH test may have low power when many, possibly high dim...
متن کاملPercolation in High Dimensions
Letpc{d) be the critical probability for percolation in Z . It is shown that lim,, _, ro 2dpc(d) = 1. The proof uses the properties of a random subgraph of an m-ary d-dimensional cube. If each edge in this cube is included with probability greater than \/2d{\ — 3/m), then, for large d, the cube will have a connected component of size cm for some c> 0. This generalizes a result of Ajtai, Komlds ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2014
ISSN: 0090-5364
DOI: 10.1214/13-aos1202