Statistics Graduate Level Quiz
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Suppose n θ^n→dZ\sqrt n\,\hat\theta_n\xrightarrow{d}Z, where Z∼N(0,σ2)Z\sim N(0,\sigma^2), and define g(x)=sin⁡(x)−xg(x)=\sin(x)-x. Which limit follows from the first nonvanishing term in the Taylor expansion of gg at zero?
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