Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics

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Conditional Linear Combination Tests for Weakly Identified Models (2016, background): “Kleibergen (2007) considers a finite-sample Gaussian IV model with a known covariance matrix for the structural errors, and his Theorem 3 establishes that (in our notation) T̃ ′T̃ = D′Σ−1D D′, where ΣD = I ( A22 A11 − ( A12 A11 )2) .”
Bootstrap inference in a linear equation estimated by instrumental variables (2008, background): “The dip is also evident in the simulation results of Stock, Wright, and Yogo (2002), which are not directly comparable to ours, since they use the same parametrization as Andrews, Moreira, and Stock (2006) and assume that Σ is known.”
Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve (2009, methodology): “At distant values of the parameters of interest, the identification robust statistics from Definition 1 correspond with statistics that test the identification of the parameters; see Kleibergen (2007, 2008) and Kleibergen and Mavroeidis (2008).”
Implementing Weak-Instrument Robust Tests for a General Class of Instrumental-Variables Models (2009, methodology): “These include the Anderson–Rubin (AR) statistic (Anderson and Rubin 1949), the Kleibergen–Moreira Lagrange multiplier (LM) test (Moreira 2003; Kleibergen 2007), the overidentification (J) test, and the conditional likelihood-ratio (CLR) test.”