基于B样条时空模型的局部众数回归

发布时间：2018-05-04 12:09

本文选题：B样条 + 局部众数回归　；参考：《东南大学》2016年硕士论文

【摘要】：在许多领域中,观测数据都与空间位置和时间点有关,这类数据被称为时空数据。关于时空数据的统计分析已经应用于经济学,大气科学等领域,具有重大的实用价值。本文基于非参数统计中的B样条方法,结合局部众数回归方法的优势,提出一种新的估计时空模型的非参数方法。该方法不仅有效解决了时空模型背景下对趋势函数的估计问题,而且相较于基于B样条的传统的最小二乘方法,在数据存在异常值或者误差服从重尾分布时,具有明显的优势；若无奇异点且误差分布是正态分布时,局部众数方法的有效性和最小二乘方法一样。此外,在所提出的基于B样条的局部众数回归模型中,应用MEM算法对模型进行模拟,比较了基于B样条的局部众数回归方法与基于B样条的最小二乘方法的优劣,同时将模型应用于实际经济数据,进一步验证了所提出方法的有效性。
[Abstract]:In many fields, observational data are related to spatial position and time points, such data are called spatiotemporal data. The statistical analysis of space-time data has been applied in economics, atmospheric science and other fields, which has great practical value. Based on the B-spline method in nonparametric statistics and the advantages of the local mode regression method, a new nonparametric method for estimating spatio-temporal models is proposed in this paper. This method not only effectively solves the problem of estimating trend function under the background of spatio-temporal model, but also has obvious advantages over the traditional least squares method based on B-spline when the data has outliers or errors distributed from the heavy tail. If there is no singularity and the error distribution is normal, the validity of the local mode method is the same as that of the least square method. In addition, in the proposed local mode regression model based on B-spline, the MEM algorithm is used to simulate the model, and the advantages and disadvantages of the local mode regression method based on B-spline and the least square method based on B-spline are compared. At the same time, the model is applied to the actual economic data to further verify the effectiveness of the proposed method.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P208;F224

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