Agenda of Week XI Review of Week X Factor analysis Illustration Method of maximum likelihood Principal component analysis Usages, basic model Objective,

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Presentation transcript:

Agenda of Week XI Review of Week X Factor analysis Illustration Method of maximum likelihood Principal component analysis Usages, basic model Objective, estimation

Review of Week X Factor analysis Illustration Method of maximum likelihood

Method of Maximum Likelihood Properties of estimators Biasedness Efficiency: Minimum variance Consistency: increasing n population Estimation of mean and variance Hogg and Craig book

Method of Maximum Likelihood Likelihood ratio function After taking logarithm to L in order to change multiplication into summation, differentiate log L with respect to theta. Find theta satisfying the above differential equations.

Method of Maximum Likelihood Example of factor analysis Factor loading matrix estimation Properties of MLS estimators Asymptotically unbiased Efficient Consistent

Principal Component Analysis Usages Academic performance Capability of baseball team Wealth of a country Data structure p variables n observations

PCA Basic model Principal component vector Common factor vector Characteristics

PCA Objective

PCA Proof.

PCA 1. Comparison between V(C i ) Trance and determinant 2. Coefficient of determination of V(C i )

PCA PCA based on correlation matrix 1. Standardization of variables 2. Calculation of eigen values and eigen vectors for correlation matrix