STATISTICAL INFERENCE IN FACTOR ANALYSIS:RECENT DEVELOPMENTS

Statistical Inference in Factor Analysis

Simultaneous Statistical Inference in Dynamic Factor Models

Based on the theory of multiple statistical hypotheses testing, we elaborate likelihood-based simultaneous statistical inference methods in dynamic factor models (DFMs). To this end, we work up and extend the methodology of Geweke and Singleton (1981) by proving a multivariate central limit theorem for empirical Fourier transforms of the observable time series. In an asymptotic regime with obse...

Procrustean statistical inference of deformations

A two step method has been devised for the statistical inference of deformation changes. In the first step of this method and based on Procrustes analysis of deformation tensors, the significance of the change in a time or space series of deformation tensors is statistically analyzed. In the second step significant change(s) in deformations are localized. In other words, they are assigned to ce...

Statistical Inference of Minimum Rank Factor Analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it...

Review of the Applications of Exponential Family in Statistical Inference

‎In this paper‎, ‎after introducing exponential family and a history of work done by researchers in the field of statistics‎, ‎some applications of this family in statistical inference especially in estimation problem‎,‎statistical hypothesis testing and statistical information theory concepts will be discussed‎.