Analysis And Application Of Generalized Partially Functional Data

With the rapid development of information technology,especially computer network technology,data information presents the characteristics of diversification,and more and more data also presents the characteristics of function.Therefore,functional data has become the focus of researchers.Functional data analysis has also been proved to be of great application value in biology,medicine,metrology and other fields.A generalized partially functional linear regression model is proposed for the regression cases where the response variables are scalar and the predictive variables are both scalar and functional.We use the functional principal component analysis method to reduce the dimension of the functional data.By means of generalized autocovariance operator,an appropriate ~2L metric corresponding to the estimation function and the real function is established.The maximum likelihood estimation method is used to solve the unknown parameter estimation of the model,and the asymptotic normality of parameter estimation is proved.We conducted a simulation study on the model,and the simulation results are consistent with the theoretical results.Finally,two application examples are given.The first was the study of sleep quality.The data of 22healthy adults on the activities and sleep of healthy people provided by Physio Net Databases was used as a case study.One is sleep quality study where we studied the efects of heart rate,percentage of sleep time on total sleep in bed,wake after sleep onset and number of wakening during the night on sleep quality.The study found that Efciency and WASO are positively correlated with sleep quality,Number is negatively correlated with sleep quality,heart rate is positively correlated with sleep quality between 8:00 and 11:00.The other one is mortality rate where we studied the efects of air quality index,temperature,relative humidity,GDP per capita and the number of beds per thousand people on the mortality rate across 80 major cities in China.The study found that GDP per capita and the number of beds per thousand people are negatively correlated with mortality rate,AQI is positively correlated with mortality in winter,early spring and fall,temperature is negatively correlated with mortality in spring,and RH is positively correlated with mortality in autumn.And according to the theory of Traditional Chinese medicine,a reasonable explanation of the results is given.These results further extend the application of generalized partially functional linear models,which laid a foundation for the research of generalized partially functional linear model of unknown connection function.