Unformatted text preview: ⇒ g ( Z n )→ g ( Z ) in probability. Z n→ Z in distribution, and g is a continuous function = ⇒ g ( Z n ) = ⇒ g ( Z ) in distribution. 5. X n→ X in probability, Y n→ Y in probability = ⇒ X n ± Y n→ X ± Y in probability; X n Y n→ XY in probability; and X n /Y n→ X/Y , if P ( Y = 0) = 0 . 6. Slutsky’s Theorem : X n→ X in distribution, Y n→ c (a constant) = ⇒ X n ± Y n→ X ± c in distribution; X n Y n→ cX in distribution; and X n /Y n→ X/c , if c 6 = 0 . * This is a very important theorem to ﬁnd the asymptotic distribution of several estimators....
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 Winter '08
 ztan
 Calculus, Topology, Derivative, Probability, Probability theory

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