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This article investigates estimation of sparsity-induced weak factor (sWF) models, with large cross-sectional and time-series dimensions (N and T, respectively). It assumes that the kth largest eigenvalue of a data covariance matrix grows proportionally to with unknown exponents for . Employing the same rotation of the principal components (PC) estimator, the growth rate α_k is linked to the degree of sparsity of kth factor loadings. This is much weaker than the typical assumption on the recent factor models, in which all the r largest eigenvalues diverge proportionally to N. We apply the method of sparse orthogonal factor regression (SOFAR) by Uematsu et al. to estimate the sWF models and derive the estimation error bound. Importantly, our method also yields consistent estimation of α_k. A finite sample experiment shows that the performance of the new estimator uniformly dominates that of the …