| 摘要: |
| 针对具有 α 混合结构的函数型时间序列数据,当响应变量随机缺失时,利用函数型单指标模型进行统计建
模,并采用 k 近邻方法对模型中未知参数和未知函数进行估计,与经典核方法相比,其数据适用性更强,可以提高
估计效率;通过数值模拟和厄尔尼诺海平面温度数据,将 k 近邻方法和经典核方法进行比较,讨论 k 近邻方法与经
典核方法对未知参数和未知函数的估计效果;从模拟结果可以看到:k 近邻方法对未知参数和未知函数的估计精度
以及随样本增加的改善效果要优于经典核方法,在真实数据分析中,k 近邻对真实数据的精度拟合以及趋势拟合都
表现优异;这些结果表明:在响应变量随机缺失的时间序列单指标模型中,采用 k 近邻方法对未知参数和未知函数
进行估计,在精度上要优于经典核方法,同时在真实数据分析中,相比经典核方法,k 近邻方法能更好地拟合
数据。 |
| 关键词: 函数型单指标模型 α 混合 k 近邻估计 随机缺失 |
| DOI： |
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HE Wenran，HUANG Zhensheng
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School of Mathematics and Statistics，Nanjing University of Science and Technology，Nanjing 210094，China
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| Abstract: |
| For functional time series data with α-mixed structure when the response variables are randomly missing the
functional single indicator model is used for statistical modeling and the k-nearest neighbor method is used to estimate the
unknown parameters and unknown functions in the model. Compared with the classical kernel method the method
proposed in this paper has better data applicability and can improve the estimation efficiency. The k-nearest neighbor
method was compared with the classical kernel method through numerical simulations and El Ni?o sea level temperature
data to discuss the estimation effects of the k-nearest neighbor method and the classical kernel method on the unknown
parameters and unknown functions. From the simulation results it can be seen that the k-nearest neighbor method
outperformed the classical kernel method in terms of accuracy of estimation of unknown parameters and unknown functions
as well as improvement with increasing samples. Moreover in the analysis of real data the k-nearest neighbor method
performed well in the accuracy fitting and trend fitting of real data. These results show that the k-nearest neighbor method
is superior to the classical kernel method in terms of accuracy in estimating the unknown parameters and unknown
functions in a single indicator model of a time series with random missing response variables. Meanwhile in the real data
analysis the k-nearest neighbor method can better fit the data than the classical kernel method. |
| Key words: functional single-indicator α mixing k-nearest neighbor estimation missing at random |
