Abstract
In the paper, we propose power weighted quantile regression(PWQR), which can reduce the effect of heterogeneous of the conditional densities of the response effectively and improve efficiency of quantile regression). In addition to PWQR, this article also proves that all the weighting of those that the actual value is less than the estimated value of PWQR and the proportion of all the weighting is very close to the corresponding quantile. At last, this article establishes the relationship between Geomagentic Indices and GIC. According to the problems of power system security operation, we make GIC risk value table. This table can have stronger practical operation ability, can provide power system security operation with important inferences.
Highlights
Weighted quantile regression is proposed by Koenker(2005)
That this paper proposes a new weighting method, that is Power Weighted Quantile Regression
In the light of the development of Quantile regression, we propose power weighted quantile regression: n min βεRp
Summary
Weighted quantile regression is proposed by Koenker(2005). When the conditional densities of the response are heterogeneous, he maintained weighted quantile regression might lead to efficiency improvements. It is considered, but reweighting based on estimated densities is somewhat difficult, that is the estimation of the weights is hard to do well, so it isn’t usually done. With regard to research weighted quantile regression, Taylor(2008) proposed exponentially weighted quantile regression and applied in Value at Risk and expected shortfall. When one independent variable value corresponding to more than one dependent variable values, the method of exponentially weight is clearly unreasonable. That this paper proposes a new weighting method, that is Power Weighted Quantile Regression
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