STATISTICAL ANALYSIS OF FACTOR MODELS OF HIGH DIMENSION

By Jushan Bai, Kunpeng Li. 2012

350 citations recorded by the source corpus.

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered. We show that the distributions of the MLE estimators depend on the identification restrictions. Unlike the principal components approach, the maximum likelihood estimator explicitly allows heteroskedasticities, which are jointly estimated with other parameters. Efficiency of MLE relative to the principal components method is also considered.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a05cf938809093b913a37a4e64712453a9b4985b

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Citations in the corpus

Theory and methods of panel data models with interactive effects (2014, methodology): “This kind of the maximum likelihood method was used for pure factor models in [3, 4] and [11].”
Certifiably Optimal Low Rank Factor Analysis (2016, methodology): “Maximum Likelihood for Factor Analysis: This approach (Bai and Li, 2012; Joreskog, 1967; Mardia et al., 1979; Roweis and Ghahramani, 1999; Rubin and Thayer, 1982) is another widely used method in FA and typically assumes that the data follows a multivariate Gaussian distribution.”
Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications (2017, methodology): “ which case the proposed estimator may not be rate optimal. In particular, when NopJq, it is known that the lower bound for the estimation of r1:N;ks can be achieved under a linear factor model (see Bai and Li, 2012). However, this lower bound may not be achievable under a generalized latent factor ”
PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS (2014, methodology): “It is often used in factor analysis for identification purposes, and means that the columns of factors and loadings can be orthogonalized (also see Bai and Li (2012)).”
Specification Test for Panel Data Models with Interactive Fixed Effects (2014, neutral): “In particular, Moon and Weidner (2010a, 2010b) and Bai and Li (2012) assume that both the factors and factor loadings are fixed constants and treat them as parameters to be estimated.”
On estimation of the noise variance in high dimensional probabilistic principal component analysis (2013, background): “There are several possibilities for the choice of such constraints; see Table 1 in Bai and Li (2012).”
Efficient Estimation of Approximate Factor Models (2012, methodology): “(i) Using the matrix inverse formula, the same argument of Bai and Li (2012)’s (A.2) implies Λ̂′(Λ̂Λ̂′ + Σ̂u) −1 = (Ir + Λ̂ ′Σ̂−1u Λ̂) −1Λ̂′Σ̂−1u .”
Item Response Theory—A Statistical Framework for Educational and Psychological Measurement (2021, neutral): “IRT models are closely related to linear factor models (see e.g., Anderson and Rubin, 1956; Bai and Li, 2012).”
Estimating High Dimensional Covariance Matrices and its Applications (2011, methodology): “The properties of the maximum likelihood estimator, under large N , is studied by Bai and Li (2010).”
Estimation and Inference of FAVAR Models (2014, methodology): “(See Bai and Li (2012) for an illustration on the sign problem.)”
Bi-cross-validation for factor analysis (2015, methodology): “The QMLE is derived by a classical factor analysis approach and it gives consistent estimation for strong factors and large data sets [4].”