Bias correction and uniform inference for the quantile density function

Grigory Franguridi

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arXiv · 2207.09004

Bias correction and uniform inference for the quantile density function

Grigory Franguridi

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Abstract

For the kernel estimator of the quantile density function (the derivative of the quantile function), I show how to perform the boundary bias correction, establish the rate of strong uniform consistency of the bias-corrected estimator, and construct the confidence bands that are asymptotically exact uniformly over the entire domain $[0,1]$. The proposed procedures rely on the pivotality of the studentized bias-corrected estimator and known anti-concentration properties of the Gaussian approximation for its supremum.

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Grigory Franguridi. 2022-07-19. Bias correction and uniform inference for the quantile density function. https://arxiv.org/abs/2207.09004

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