Some Multivariate Statistical Analysis Methods And Its Simple Applications

The multivariate statistical analysis is developed from the classic statistical theory,which is based on the normal distribution. It is a comprehensive analysis method that re-search the interrelation of multivariate random variables and its own statistical regularity,In order to study the relationship between multivariate random variables and provide astrong theoretical support. This paper introduce the some relevant properties of the prin-cipal components in the principal component analysis in details; In the factor analysis, Weselect likelihood estimation method to obtain the loading matrix and special factor vari-ance; we give some ways of defining distance in hierarchical cluster; And in the canonicalcorrelation analysis, we are committed to seeking for the canonical correlation variables. And we take advantage of these four methods to make a simple empirical applicationabout the consumption structure of rural residents in the family.There are six chapters in this full paper:In the first chapter,we mainly introduce the background of multivariate statisticalanalysis methods application, the researching status of domestic and foreign, and alsothe methods which we use in this paper.In the second chapter, we firstly briefly describe the thought of principal compo-nent,and secondly mainly introduce the solving method and some important propertiesof principal components; At last, we extract the principal component of rural residents’consumption structure in our country from2007to2012，and at the same time,we makesome appropriate interpretation and analysis.The third chapter is one of important part of this article, Firstly, we introduce theorthogonal factor model; Secondly, we demonstrate the theoretical derivation process ofmaximum likelihood estimation method for factor loadings matrix and special factor vari-ance, Not only we improved the previous proof, but also make up for the deficiency thatinterpretation of results are not clear by using factor models for empirical analysis; Third-ly, we give the statistically significant of the factor loading matrix of orthogonal factormodel and the test statistic of the covariance matrix; At last, we apply this model into thedata we search, and we need72iterations achieve the convergence value by selecting theappropriate initial value, and find that the factor model we construct is very reasonable through hypothesis testing.In the fourth chapter, we firstly introduces some definitions of distance in commonuse of the hierarchical cluster method; Secondly, We choose the hierachical cluster anal-ysis method to classify31provinces into3categories of our country.The fifth chapter is another important aspect in this paper, At the beginning of thischapter, We give a brief introduction about the role and status of canonical correlationvariables, and elaborates the derivation of canonical correlation variables by gradually;Secondly, we give the proof of number of canonical correlation variables hypothesis teststatistic; At last, we introduce the typical correlation structure and canonical redundancyanalysis in order to give a reasonable interpretation of canonical correlation variables. wegive a summary of the article and some similar problems in the sixth chapter in the futureoutlook.