This paper proposes a model-free nonparametric estimator of conditional quantile of a time series regression model where the covariate vector is repeated many times for different values of the response. This type of data is abound in climate studies. To tackle such problems, our proposed method exploits the replicated nature of the data and improves on restrictive linear model structure of conventional quantile regression. Relevant asymptotic theory for the nonparametric estimators of the mean and variance function of the model are derived under a very general framework. We provide a detailed simulation study which clearly demonstrates the gain in efficiency of the proposed method over other benchmark models, especially when the true data generating process entails nonlinear mean function and heteroskedastic pattern with time dependent covariates. The predictive accuracy of the non-parametric method is remarkably high compared to other methods when attention is on the higher quantiles of the variable of interest. Usefulness of the proposed method is then illustrated with two climatological applications, one with a well-known tropical cyclone wind-speed data and the other with an air pollution data.
翻译:本文建议对一个时间序列回归模型的有条件的量化进行一个无模型的非参数性估计,即共变矢量为不同响应值多次重复。这种类型的数据在气候研究中很多。为了解决这些问题,我们建议的方法利用数据的复制性质,改进传统孔数回归的限制性线性模型结构。对于该模型平均值和差异函数的非参数性估计器,相关的非参数性理论是在一个非常笼统的框架内得出的。我们提供了详细的模拟研究,清楚地表明了拟议方法相对于其他基准模型的效率的提高,特别是当真正的数据生成过程包含非线性平均功能和与时间相关的共变异的恒变模式时。当关注利益变量的较高孔性时,非参数性方法的预测准确性与其他方法相比非常高。然后用两种气候学应用对拟议方法的实用性加以说明,一种是已知的热带气旋风速数据,另一种是空气污染数据。