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Linear-in-Parameter Model with Non-iid Settings

The general form of a linear quantile regression model is

where the iid assumption is not necessary. Under some regularity conditions, the asymptotic distribution of the general form
of quantile regression estimates is

where

Accordingly, the covariance matrix of can be estimated as

where .

The sparsity value of the ith observation, , can be estimated as

where are the ith predicted quantile values at quantile levels .