A new bias reduction method for kernel extreme quantile function estimation

Abstract

Quantiles are frequently used to assess risk across a wide range of applications, especially for extreme risks, such as in finance and service industries. In this paper, a new estimator for kernel quantile estimation is proposed to reduce boundary bias. The asymptotic properties of the proposed estimator are established, and it is shown that the bias is reduced to the fourth power of the bandwidth, whereas the bias of the classical kernel quantile function estimator is the second power of the bandwidth. Moreover, the variance remains on the same order as the classical estimator. A numerical study is conducted to evaluate finite-sample performance.

Keywords

• Bias reduction
• kernel estimation
• mean squared error
• quantile function

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