Investment Income Research Functional Data Analysis

The statistical data fitting is one of the important topics and long, traditionalstatistical analysis methods such as linear regression, multivariate statistics, we mostlydeal with discrete data objects, and our common data types, including time-series data,cross-section data or a combination of both that panel data. However, practicalproblems, in fact a lot of statistical data generated can be used to approximate afunction expression to describe, but the information obtained by traditional statisticalmethods are often fragments of discrete number of columns, which undoubtedly lost alot of useful information to statisticians door can imagine these discrete functionsfitted to the observed data, to in-depth study of the nature of the function object reusegood from the perspective of mathematics, which undoubtedly is the statisticalanalysis in the field to open up a new way of thinking.We are going to introduce roughly function type data analysis methods in thisarticle, the data obtained by the fitting function is mostly a function of the system isachieved through the base, and has many excellent properties. The parameters used inthe traditional method of least squares estimation may be accompanied by over-fittingand, therefore, we will be corrected, and the introduction of the concept of smoothingparameter matrix and smooth after its application to parameter estimation offunctional data analysis. Once you have the fitting function, we were to introduceclassical theory of multivariate statistical analysis of variance, principal componentanalysis and canonical correlation analysis was used to analyze how the expandedfunction type data. In addition, in the empirical analysis, we will adopt a concreteexample to illustrate functional data analysis methods, especially in the financialsector investments in securities of applications.