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§ 13. Hypothesis testing asymptotics II Setup: H0 ∶X n ∼ P n ∶ X X n n ecification: → H1 ∶X ∼ QX (i.i.d. test PZ ) ∣ n Xn n sp { n 0,1 1 − α = π ( 2 1…

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13 Large Sample Tests 13.1 Wald, LM and LR Tests Parameter θ : k × 1, hθ : G × 1 vector function, G ≤ k The null hypothesis H0 : hθ = 0 =⇒ G restrictions θ̃ :…

Chapter 13 Partial Derivatives 131 Functions of Several Variables 1 {x yx y 6= 0 0} 2 {x yx 6= x± 3y} 3 {t Y y 6= x2} 4 {x yy ≥ −4} 5 {s ts t any real numbers} 6 {u…