Efficient Estimation Of Approximate Factor Models Via Regularized Maximum Likelihood
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Efficient Estimation of Approximate Factor Models Via Regularized Maximum Likelihood
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the factor loadings or common factors because it essentially treats the idiosyncratic error to be homoskedastic and cross sectionally uncorrelated. For the efficient estimation, it is essential to estimate a large error covariance matrix. We assume the model to be conditionally sparse, and propose two approaches to estimating the common factors and factor loadings; both are based on maximizing a Gaussian quasi-likelihood and involve regularizing a large covariance sparse matrix. In the first approach the factor loadings and the error covariance are estimated separately while in the second approach they are estimated jointly. Extensive asymptotic analysis has been carried out. In particular, we develop the inferential theory for the two-step estimation. Because the proposed approaches take into account the large error covariance matrix, they produce more efficient estimators than the classical PCA methods or methods based on a strict factor model.
Statistical Foundations of Data Science
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
The Elements of Financial Econometrics
Author: Jianqing Fan
language: en
Publisher: Cambridge University Press
Release Date: 2017-03-23
A compact, master's-level textbook on financial econometrics, focusing on methodology and including real financial data illustrations throughout. The mathematical level is purposely kept moderate, allowing the power of the quantitative methods to be understood without too much technical detail.