Summary
The video discusses various methods for estimating L and psi in a factor model, such as the principal component method and maximum likelihood estimation. It explores Eigenvalues in the delta matrix and the contribution of factors to sample variance. Maximum likelihood estimation involves deriving the likelihood function and estimators of L and psi using specified distributional assumptions. The video explains the likelihood ratio test for determining the number of common factors in factor analysis, considering degrees of freedom and criteria for rejecting the null hypothesis.
Methods of Estimation in Factor Model
Discussion on methods of estimation of L and psi in a factor model, including the principal component method and the closeness of approximation.
Eigenvalues and Approximation Bounds
Exploration of Eigenvalues in the delta matrix and the bound on the approximation of S in the principal component method.
Sample Variance Contribution
Analyzing the contribution of factors to sample variance in the principal component-based method of estimation.
Maximum Likelihood Estimation
Introduction to maximum likelihood estimation of L and psi in a factor model, assuming a multivariate normal distribution.
Likelihood Function and Estimators
Deriving the likelihood function and estimators of L and psi using maximum likelihood estimation under specified distributional assumptions.
Maximum Likelihood Estimators
Determining maximum likelihood estimators of L and psi with mu hat estimator in the factor model.
LR Test for Common Factors
Explaining the likelihood ratio test for determining the number of common factors in factor analysis based on maximum likelihood estimators.
Degrees of Freedom and Rejection Criteria
Understanding degrees of freedom in the likelihood ratio test and the criteria for rejecting the null hypothesis.
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