Quantile Estimation of A general Single-Index Model
نویسندگان
چکیده
Regression quantiles, along with the dual methods of regression rank scores, can be considered one of the major statistical breakthroughs of the past decades. Its advantages over the other estimation methods have been well investigated. Regression quantile methods provide a much more complete statistical analysis of the stochastic relationships among variables; in addition, they are more robust against possible outliers or extremely values, and can be computed via traditional linear programming methods. Although median regression ideas go back to the 18th century and the work of Laplace, regression quantile methods were first introduced by Koenker and Bassett (1978). The linear regression quantile is very useful, but like linear regression it is not flexible to capture complicated relations. For quantile regression, this disadvantage is even worse. As an example, consider the popular AR(1)-ARCH(1) model:
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