### Huixia Judy Wang - Inference for High Dimensional Quantile Regression

### 2 Answers

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In the discussion of McKeague & Qian (2015), Shah & Samworth suggested that since the global null had such a simple form, then the test statistic could be calibrated using permutations. Your setting is obviously very different, but does some modification of that approach work for calibration? On your slide 12, it seems to suggest that this simplification might also arise here?

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**Permutation may be ok for homoscedastic cases. However, for heteroscedastic cases the regression error may depend on the covariates there will be issues with permuting the covariates by rows, and quantile regression in general has more advantages for heteroscedastic cases.**

written
9 months ago by
Judy Wang

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This is a bit off-toic, but is there an issue of lack of smoothness when applying the bootstrap to quantile regression?
A short answer is no since the bootstrap works when the estimator is asymptotically linear. For quantile regression, the coefficient estimator has a Bahadur (asymptotic) linear representation. Of course there may be some issues for very extreme quantiles, i.e. when the quantile level=0/1 or approaches 0/1 at a very fast rate.

written
9 months ago by
Judy Wang

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