Nonparametric Estimation Of Gaussian Processes

This paper mainly studies two estimation methods of Gaussian sequence model under communication constraints proposed by Cai and Wei[9],which are Minimax optimal estimation and local threshold optimal adaptive estimation..Firstly,according to the idea of distributed estimation,an optimal program is proposed and the optimal convergence rate of the algorithm under the communication constraint is deduced by minimax method.The optimal adaptive estimation based on local threshold is an improvement to realize the adaptive performance on a wide range of Besov spaces.By giving a quantitative description of the communication cost,the optimality and adaptive performance of the algorithm can be obtained.Through data simulation,we show that these two estimates have better statistical performance,and local threshold estimation has better adaptability.The first chapter introduces some basic knowledge and assumptions,the second and third chapters respectively introduce the two estimation algorithms and describe the communication cost and convergence rate,the fourth chapter shows the numerical simulation results,and finally the fifth chapter summarizes and prospects.