Statistics Graduate Level Quiz
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ASYMPTOTIC THEORY
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In the scalar regression model Y=Xβ0+εY=X\beta_0+\varepsilon, consider the M-estimating equation ∑i=1nXiψ(Yi−Xiβ)=0\sum_{i=1}^n X_i\psi(Y_i-X_i\beta)=0 for a nonlinear score ψ\psi. Which condition most directly guarantees that the population estimating equation is unbiased at β0\beta_0 for arbitrary distributions of XX?
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