Author : Linquan Ma (Ph.D.)
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Book Synopsis Dimension Reduction in Statistical Modeling by : Linquan Ma (Ph.D.)
Download or read book Dimension Reduction in Statistical Modeling written by Linquan Ma (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the data object is described by a large number of features, it is often beneficial to reduce the dimension of the data, so that the statistical analysis can have better efficiencies. Recently, a new dimension reduction method called the envelope method by Cook, Li, and Chiaromonte (2010) has been proposed in multivariate regressions. It has the potential to gain substantial efficiency over the standard least squares estimator. Chapter 2 proposes an approach to use the envelope method when the predictors and/or the responses are missing at random. When there exists missing data, the envelope method using the complete case observations may lead to biased and inefficient results. We incorporate the envelope structure in the expectation-maximization (EM) algorithm. Our method is guaranteed to be more efficient, or at least as efficient as, the standard EM algorithm. We give asymptotic properties of our method under both normal and non-normal cases. Chapter 3 extends the envelope model to the mixed effects model for longitudinal data with possibly unbalanced design and time-varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Chapter 4 proposes a semiparametric variant of the inner envelope model (Su and Cook, 2012) that does not rely on the linear model nor the normality assumption. We show that our proposal leads to globally and locally efficient estimators of the inner envelope spaces. We also present a computationally tractable algorithm to estimate the inner envelope. The instrumental variables (IV) are frequently used in observational studies to recover the effect of exposure in the presence of unmeasured confounding. A key fact is that the strength of IV matters: an IV with a stronger association with the exposure results in a more accurate estimation of a causal effect. While it is hard to find a stronger IV, we generalize a sufficient dimension method to remove immaterial IVs. Chapter 5 investigates two different ways of incorporating the envelope method into IV regression. We show that the first stage envelope method does not yield any efficiency gain on the standard IV estimator, however, it may reduce the finite sample bias. The second stage envelope can achieve substantial efficiency gain under certain conditions.
