2016
DOI: 10.1111/rssb.12166
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Estimation of High Dimensional Mean Regression in the Absence of Symmetry and Light Tail Assumptions

Abstract: Data subject to heavy-tailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and Least Absolute Deviation (LAD) regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression functions in… Show more

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Cited by 179 publications
(178 citation statements)
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“…For example, to estimate the stock network, it is more meaningful to take out the common market factors from the return data and study the conditional independence relationships between idiosyncratic components; in genomics, the conditional independence graph after taking the confounding factors such as age and environment exposure are of better interest. The factors can also be interpreted as covariates to be adjusted before analyzing the correlatedness of the residual part (Fan et al, 2016). Rothman, Levina and Zhu (2010) and Cai et al (2013) adopted the same idea of adjusting the factors in predicting asset returns and analyzing genomics data, but they do not impose the pervasiveness condition, instead they need to impose the constraint of a sparse factor loading matrix B .…”
Section: A High-level Theoretical Interfacementioning
confidence: 99%
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“…For example, to estimate the stock network, it is more meaningful to take out the common market factors from the return data and study the conditional independence relationships between idiosyncratic components; in genomics, the conditional independence graph after taking the confounding factors such as age and environment exposure are of better interest. The factors can also be interpreted as covariates to be adjusted before analyzing the correlatedness of the residual part (Fan et al, 2016). Rothman, Levina and Zhu (2010) and Cai et al (2013) adopted the same idea of adjusting the factors in predicting asset returns and analyzing genomics data, but they do not impose the pervasiveness condition, instead they need to impose the constraint of a sparse factor loading matrix B .…”
Section: A High-level Theoretical Interfacementioning
confidence: 99%
“…In addition, Hampel (1974); Rousseeuw and Croux (1993); Koenker (2005) considered the problem from a quantile perspective. In this section, we introduce two M-estimators proposed by Fan, Li and Wang (2016) and Catoni (2012). The methods allow asymmetric distributions, and thus are also useful for robust estimation of variances.…”
Section: Elliptical Factor Modelsmentioning
confidence: 99%
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“…In practice, we can use, for example, the average version to estimate the scaling factor. We could also replace the sample standard deviation estimator by the Catoni's M-estimator (Catoni, 2012) or less biased robust approximate quadratic (RA-quadratic) estimator (Fan et al, 2016), which are appealing alternatives in handling heavy-tailed data.…”
Section: Remark 23mentioning
confidence: 99%