【统计学论坛】高维尺度不变的判别分析

Abstract: This paper considers a three-dimensional latent factor model in the presence of one set of global factors and two sets of local factors. We allow the numbers of local factors to vary across individuals and show that the numbers of global and local factors can be estimated uniformly consistently. Given the number of global and local factors, we propose a two-step estimation procedure based on principal component analysis (PCA). Our first step estimates the global factors and their factor loadings, after which we estimate the two sets of local factors and factor loadings sequentially. Our second step improves the estimation efficiency. The asymptotic theories for our estimators are established. Monte Carlo simulations demonstrate that they perform well in finite samples. Applications to two datasets in international trade and economic growth reveal the relative importance of different types of factors. In the international trade application, we find that the global factors, source country factors, and destination country factors are all important. In the industrial growth application, there is no global factor and the country factors are far more important than the industry factors. The extension to the 3D factor model with covariates is also studied.