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Abstract:
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We propose a quantile estimate that is robust to two types of atypical observations in the design space: one is outlying covariates, known as high-leverage points; another type may not have manifested itself in any single component of $X$, but clearly deviated from the majority of the data. When the design space has certain structures other than ellipse, the second type outliers may be hidden by the existing algorithms assuming generic distribution. We propose a new data-adaptive method to quantify the deviations of a single observation in the design space, and incorporate them into the quantile regression estimation equations to achieve robust quantile estimates. The resulting quantile estimates have bounded influence, and are asymptotically consistent and normally distributed; the methodologies are applied to robustify conditional weight screening model based real Finnish growth data.
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