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

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Review of Week X Factor analysis Illustration Method of maximum likelihood

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

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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.

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

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

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PCA Basic model Principal component vector Common factor vector Characteristics

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PCA Objective

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PCA Proof.

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

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

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