STATISTICAL INFERENCE IN PRINCIPAL COMPONENT ANALYSIS BASED ON STATISTICAL THEORY

Abstract

Principal component analysis is a diversified statistical method, while statistical inference is the major research subject in modern statistics, whose theories and methods have comprised the core content of mathematical statistics.  According to the relevant knowledge of statistical theory and based on a large sample size, this study explored the statistical inference problem when population followed normal distribution.  Besides, statistical methods were applied to further analyze the statistical inference problems in principle component analysis under the condition of population with non-normal distribution or small sample size.  First, principal component analysis was performed on parameter estimation and hypothesis testing on the condition that population followed multivariate normal distribution.  Then under the condition of complex distribution of population, simulated sampling statistical inference method, i.e., Bootstrap method, was used to do interval estimation and discuss over other statistical inference problems of the characteristic values of the correlation coefficient matrixes in principle component analysis, and then the defects of Bootstrap method were adjusted using Bayesian theory.