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Bai (2009) proposes a recursive least-squares estimation method for large panel data models with unobservable interactive fixed effects, but the impact of recursion on the asymptotic properties of the least-squares estimators is not taken into account. In this paper, we extend Bai ( 2009) by investigating the recursive estimator asymptotically. In general, the asymptotic properties we establish for the recursive estimators largely complement the theory and practice of the recursive least-squares procedure suggested by Bai (2009). In particular, we show that consistency of the recursive estimator depends on three key points, consistency of the initial OLS estimator, the number of recursive steps and the endogeneity arising due to the dependence between regressors and interactive effects. Compared to the theoretical estimator in Bai ( 2009), such endogeneity affects the convergence rate of recursive least-squares estimators. Finite sample properties of the proposed estimators are investigated using a simulation study.

In this paper, we obtain the unified error estimate for some weak biorthogonal greedy algorithms with respect to dictionaries in Banach spaces by using some kind of [Formula: see text]-functional. From this estimate, we derive the sufficient conditions for the convergence and the convergence rates on sparse classes induced by the [Formula: see text]-functional. The results on convergence and the convergence rates are sharp.

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