Most of the existing estimation methods for linear models are based on mean regression by least squares or likelihood method. However, these methods are sensitive to outliers and may not be effective for many irregular errors. Quantile regression (QR) is more robust in exploring the relationship between covariates and dependent variables.
The utility of the Lp-quantile as an extension of quantile and expected quantile, the validity of the quantile regression and the expected quantile regression method have been demonstrated and many studies have been conducted, but the asymptotic properties of the Lp-quantile regression estimators have not been fully considered.
Jo Chol Min, a researcher at the Faculty of Applied Mathematics, has considered the Lp-quantile regression estimation of unknown parameters in a linear model and proved the asymptotic normality of the Lp-quantile regression estimator for different p.
The results show that when 1/2>p>0, the convergence rate of the estimator is slower than that of the usual case, and that if p>1/2 and other certain regularity conditions hold, the estimator is asymptotically normal at n1/2-rate. (See Figure)
The results can be effectively used to solve practical problems such as interval estimation or hypothesis testing.
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