Efficiency of projected score methods in rectangular array asymptotics

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Estimating Dynamic Panel Data Discrete Choice Models with Fixed Effects (2007, background): “Li et al. (2003), consider a different adjustment to the MLE and derive its double asymptotic properties, too.”
Split-Panel Jackknife Estimation of Fixed-Effect Models (2015, background): “…of more observations per unit does not necessarily solve the inference problem, however, because confidence intervals centered at the maximum-likelihood estimate are incorrect under rectangular-array asymptotics, i.e., as N,T → ∞ at the same rate (see, e.g., Li, Lindsay, and Waterman 2003).”
Asymptotics for panel quantile regression models with individual effects (2012, methodology): “This means that, in contrast to estimators with smooth objective functions that have been studied in the literature such as Li, Lindsay, and Waterman (2003), Hahn and Newey (2004) and Fernandez-Val (2005), the Taylorseries methods of asymptotic distribution theory do not apply to the FE-QR…”
Smoothed quantile regression for panel data (2015, unknown): “In particular, to our knowledge, whether the asymptotic results analogous to those of Li, Lindsay, and Waterman (2003) or Hahn and Newey (2004) hold forˆβ KB is not known.”