Nearest Neighbor Estimation And Application Of Functional Data Nonparametric Model Based On Dependent Sequences

Compared to the independent sample,the sample of functional dependent structure sequence has been extensively used in various fields,including mathematical statistics,reliability theory and financial economics.Currently,the theory of the functional data based on the independent sample has been relatively mature.In contrast,there is a lack of studies on the dependent sample in previous research work.It is of great worthy to investigate and reveal the asymptotic property in the theory and practice.For instance,the studies of the functional data of dependent structure,based on the negatively associated(NA)sequence which is one of crucial dependent sequences,are worth for the further development.Additionally,the nonparametric regression model has an attracted attention in the statistical model estimation since it has advantages of the unrequired population distribution,flexible and various estimation approaches,and excellent robustness.The k-nearest neighbor(kNN)estimator based on the kernel density estimator has excellent advantages in theory results and prediction performance,so it has gradually become one of the effective tools for studying functional data.In this paper,firstly,the moment inequality and truncation thought were adopted to investigate the weak convergence of the random sum of NA arrays.Subsequently,the kNN estimator was used to estimate the nonparametric model which was based on the functional data of the NA dependent sequence.The uniform convergence property of kNN estimator was discussed as well as the uniform complete convergence speed of the kNN estimator was acquired,and related inequalities and existing conclusions were introduced to verify the theorem in detail.Finally,the finite sample simulation and actual data were used to verify the effectiveness of the model estimation results,respectively.The fitting effect,comparing with the traditional kernel density estimation method was to verify the practical value of the model estimation.