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IAbstract
Abstract
With the progress of science and technology, it is easy to obtain data. The direct conse-
quence is that the obtained data show the characteristics of large quantity and high dimension,
and the curse of dimensionality often occurs. To deal with this problem and obtain more in-
formation, the most effective method is to reduce the dimension of data. In many applications,
especially in economics, data analysis usually includes various structural indicators, and the mea-
sured data of these indicators are collected from countries (regions) every year (monthly), which
falls into the formation of longitudinal compositional data. Huge data dimension makes the s-
tatistical analysis of longitudinal compositional data difficult. Considering sufficient dimension
reduction has the advantages of not losing regression information and maintaining the internal
structure of data , this paper uses this idea to conduct the sufficient dimension reduction on lon-
gitudinal compositional data.
Before dimension reduction, this paper first introduces a ser