Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the former approach may suffer from the bias while the latter can not incorporate additional information. We propose to bridge these two approaches while allowing the number of factor proxies to diverge, and hence make the latent factor model estimation robust, flexible, and statistically more accurate. As a bonus, the number of factors is also allowed to grow. At the heart of our method is a penalized reduced rank regression to combine information. To further deal with heavy-tailed data, a computationally attractive penalized robust reduced rank regression method is proposed. We establish faster rates of convergence compared with the benchmark. Extensive simulations and real examples are used to illustrate the advantages.
翻译:长期要素模型估计通常依靠利用域知识手工挑选几个观察到的共同变量作为要素替代物,或纯粹进行多种变量分析,如主要组成部分分析,但前者可能存在偏差,而后者不能纳入更多的信息。我们提议弥合这两种方法,同时允许要素替代物的数量出现差异,从而使潜在要素模型估计更加有力、灵活和统计上更加准确。作为一种红利,还允许因素数量增长。我们方法的核心是减少排名回归以惩罚合并信息。为了进一步处理重尾数据,我们提议采用具有计算吸引力的、惩罚性强势的低级回归法。我们建立了比基准更快的趋同率。我们使用广泛的模拟和真实例子来说明其优点。