| This paper first introduces the concept of statistical optimization problems,which refers to the process of improving the solution of certain statistical problems with optimization ideas or methods.Systematically classify a series of optimization and algorithm improvement problems in statistics.These problems are classified according to the correlation with statistical optimization knowledge,and are divided into statistical method optimization,statistical model optimization,and statistical algorithm optimization.Then,the knowledge involved in these three optimizations is compared and analyzed,and the statistical and optimization ideas are the most in-depth in statistical algorithm optimization.However,in the optimization of statistical algorithms,it is divided into basic research and applied research according to different fields and directions.Finally,we get certain enlightenment,we should pay attention to the running time and efficiency of the algorithm,the global convergence of the algorithm,the convergence speed and complexity.Next,it is explained that the maximum likelihood estimation in point estimation is a more typical optimization problem,and the relevant knowledge of optimization can be applied in the construction and solution algorithm of the model.The optimization principle in the solution process of maximum likelihood estimation is pointed out,and the algorithm research process for solving maximum likelihood estimation is expounded.The lookout algorithm and its improvement method are given,and the improved lookout algorithm is evaluated,which proves that the improved algorithm has high solution performance for solving functions with more local optimal solutions.Then,the lookout algorithm is used to solve the factor analysis model with factors following the exponential distribution,and it is shown that it has better solution performance through comparison.It is also verified that in the optimization of statistical algorithms,different optimization methods can be used to solve the solution,and then a more accurate solution can be obtained.Finally,for the current researchers,mainly on the improvement and application of the lookout algorithm,there is a lack of systematic theoretical analysis of the lookout algorithm,and the lookout algorithm itself has no general convergence proof.In this paper,the state transition probability of the lookout point is improved according to the cyclic calculation process of the lookout algorithm,and the Markov chain model of the lookout algorithm is established and analyzed mathematically.Next,it is proved that the resulting sequence is a homogeneous finite Markov chain and satisfies the stability condition,so as to prove that the lookout algorithm converges to the global optimal with probability 1,and the convergence proof of the algorithm is obtained. |
