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 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 Inferences Using Large Estimated Covariances for Panel Data and Factor Models

While most of the convergence results in the literature on high dimensional covariance matrix are concerned about the accuracy of estimating the covariance matrix (and precision matrix), relatively less is known about the effect of estimating large covariances on statistical inferences. We study two important models: factor analysis and panel data model with interactive effects, and focus on the statistical inference and estimation efficiency of structural parameters based on large covariance estimators. For efficient estimation, both models call for a weighted principle components (WPC), which relies on a high dimensional weight matrix. This paper derives an efficient and feasible WPC using the covariance matrix estimator of Fan et al. (2013). However, we demonstrate that existing results on large covariance estimation based on absolute convergence are not suitable for statistical inferences of the structural parameters. What is needed is some weighted consistency and the associated rate of convergence, which are obtained in this paper. Finally, the proposed method is applied to the US divorce rate data. We find that the efficient WPC identifies the significant effects of divorce-law reforms on the divorce rate, and it provides more accurate estimation and tighter confidence intervals than existing methods

The upper limit of the e+e- partial width of X(3872)

The e+e- decay partial width of the recently observed state, X(3872), is estimated using the ISR data collected at the center of mass energy 4.03 GeV in e+e- annihilation experiment by BES at BEPC. It is found that the product of the e+e- partial width and X(3872) --> pi+ pi- J/psi decay branching fraction is less than 10 eV at 90 % confidence level if the J(PC) of X(3872) is 1(--). Together with the potential models and other information, we conclude that X(3872) is very unlikely to be a vector state.Comment: 5 pages, 1 figur

Recent BES Results on Hadron Spectroscopy

We present recent results from the BES experiment on the observation of the Y(2175) in J/\psi\to \phi f_0(980) \eta, study of \eta(2225) in J/\psi\to \gamma \phi \phi, and the production of X(1440) recoiling against an \omega or a \phi in J/\psi hadronic decays. The observation of \psi(2S) radiative decays is also presented.Comment: 5 page