Bootstrap procedures for dynamic factor analysis.
Guangjian Zhang · OhioLink ETD Center (Ohio Library and Information Network) · 2006
Dynamic factor analysis (DFA), a combination of factor analysis and time series analysis, involves autocorrelation matrices calculated from multivariate time series.Because the distribution of autocorrelation matrices is intractable, it is difficult to obtain statistical properties of DFA estimators.The dissertation proposes using the bootstrap to obtain standard error estimates, confidence intervals, and test statistics for DFA models.In efforts to accommodate the dependence between data at different time points, two bootstrap procedures for dependent data, namely the parametric bootstrap and the moving block bootstrap, are employed.The parametric bootstrap is like a Monte Carlo study in which the population parameters are the parameter estimates obtained from the original sample.The moving block bootstrap breaks down the original time series to blocks, draws samples with replacement from the blocks, and connects the sampled blocks together to form a bootstrap sample.In addition, the dissertation considers DFA with categorical data which is common in psychological research.Bootstrap confidence intervals and bootstrap tests require quantiles of the distribution of bootstrap replications.The quantiles are often estimated using empirical cumulative distribution functions (CDF).The target distribution method is a semiparametric method for estimating distribution functions.This dissertation also I express the deepest appreciation to Dr. Michael Browne for his advice, guidance