The study of this theoretical problem enables sparse or dense functional data, including educational information evaluation data. The choice of different weights is subjected to principal component analysis. The evaluation of music education informatization level mainly evaluates the status quo of music education informatization development, provides a basis for formulating and adjusting music education informatization development policies, and provides support for educational decision-making, to promote the sustainable and balanced development of music education informatization. The evaluation of music education informatization has become the key promotion work of music education informatization at this stage. This paper studies the convergence rate of functional principal components based on the local linear method under general weighting conditions. First, we introduce the related research on the estimation of mean and covariance function under general weighting. Secondly, for principal functional components under general weighting, namely, eigenvalues and eigen functions, the text gives the corresponding estimated values and derives its strong uniform convergence rate. Finally, the convergence rate was verified by simulation research. The estimation methods and conclusions of this article enrich the research of functional linear regression models and will help analyze the complex and changeable problems encountered in the application of music education information.
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