Analysis Of Robust Functional ANOVA Model With T Process

Nowadays,with the development of science and technology,multivariate statisti-cal data analysis has become a hot topic for statisticians to study,and functional data analysis has become an indispensable aspect of statistical data analysis due to its uni-versality and importance.Research topic in the field of functional data analysis is very broad,mainly including functional data registration,canonical correlation,principal component analysis,discriminant analysis and regression model.Among them,the functional ANOVA model has its own place because of its wide application.For this model,we study its robust estimation,discuss its statistical property and evaluate its predictive ability.First of all,in the traditional functional ANOVA model,the error term mostly fol-lows the Gaussian process,which make the model more sensitive to outliers,in some practical cases,this will affect the model's fitting effect and prediction accuracy.There-fore,in order to reduce the sensitivity of model to outliers,a robust functional ANOVA model based on extended t process is proposed in this paper.Furthermore,in the model,we introduce the random effect function to describe the individual characteristics of the research object,which further improves the prediction accuracy of the model.Based on this,we propose a prediction method of functional ANOVA model,especially the prediction of individual effects.Secondly,most of the functional ANOVA models assume that the response curves are independent without considering the correlation between the curves.But in the ac-tual cases,such as the product penetration data mentioned in the paper,in different coun-tries within the same region,the trend of economic development level and national con-sumption level is similar,the data has a high correlation.It is obviously different from the actual situation to process data as individuals.Therefore,in order to describe the dependence between curves and ensure the positive definiteness of the covariance func-tion,this paper introduces random effect variable and convolution method to construct a covariance function,then proposes a dependent robust functional ANO VA model with t process and establishes the estimation and prediction methods of this model.Finally,for the two models mentioned above,the overall influence of individual effect on the model is considered in this paper,which makes the model have better properties.In this paper,the Gaussian approximation method is used to simplify the calculation of complex integrals.This paper studies the statistical properties including robustness and information consistency,and the results of numerical simulation and case analysis show that the two models have nice fitting and prediction ability.In addition,we explore the influence of the selection of smoothing splines and covariance kernels on the model prediction in functional ANOVA model.