Research On Statistical Inference Of The Principal Components Analysis

As the basic method of the modern statistics,statistical inference iswidely used instatistical research. It can be used either for the overallparameters estimation, or can be used in some of the overall distributioncharacteristics to test the hypotheses. The principal component analysis isa widely used method of multivariate statistical analysis.In the principalcomponent analysis, it is usually difficult to derive a total principalcomponent directly. Therefore, it needs to use the sample to estimate themain component of the overall principal components.This is related tostatistical inference problems in the principal component analysis.In this paper, we used statistics,Bayes statistics, knowledge andtheory in sampling technologies, in order to summarize and perfet thenormal distribution of principal components analysis which based on alarge sample of conditions in general statistical inference.Also,we tried touse the Bootstrap method, Jackknife method and adjusted Bootstrapmethod based on Bayes ideas,which in the case of complex distribution ofthe overall (non-nomal population) or small samples, to make thereasearch on the principal component analysis of statistical inference toimprove and optimize the the principal component analysis statisticalinference problems.In this article,we first collated and summarized the statistical inferenceof the principal components analysis method in the condition of the large sample and the overall which subjected to the multiple normaldistribution hypothesis, including parameters estimation and hypothesistesting.The parameter estimation is divided into three parts:looking foreigenvalue and eigenvector of approximate distribution,constructing theconfidence interval of eigenvalue and the confidence domain of theeigenvectors,and constructing the joint confidence interval of theprincipal component score. Hypothesis test is divided into three parts:thetest of the characteristics of the principal component analysis,theinspection of the characteristic roots,the test of selecting the number ofthe principal component and so on.Secondly, the article mainly talked about the statistical inference ofthe principal component analysis,which based on the conditions of thecomplex general distribution, or the unknown general distribution underthe premise.First we used two statistics inference methods:the Bootstrapmethod and the Jackknife method,to talk about the interval estimates ofthe correlation coefficient matrix eigenvalue and other statistics inferenceproblems of principal component analysis.At the same time,we took intoaccount the advantages of the two methods,estimated errors,defects andother problems,including the use of the Bayes idea to adjust thecorrection of the Bootstrap method,which will combine the Bayesmethods and Bootstrap methods to the component analysis in statisticalinference, Finally,we contacted and compared all the estimates methods,andgot a summary of this paper as well as the description of the contents ofthe follow-up study。...