Transcription of Lecture Notes 9 Asymptotic Theory (Chapter 9)
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Lecture Notes 9 Asymptotic Theory (Chapter 9)
Lecture Notes 9. Asymptotic Theory (Chapter 9). In these Notes we look at the large sample properties of estimators, especially the maxi- mum likelihood estimator . Some Notation: Recall that Z. E (g(X)) g(x)p(x; )dx. 1 Review of o, O, etc. 1. an = o(1) mean an 0 as n . P. 2. A random sequence An is op (1) if An 0 as n . P. 3. A random sequence An is op (bn ) if An /bn 0 as n . P. 4. nb op (1) = op (nb ), so n op (1/ n) = op (1) 0. 5. op (1) op (1) = op (1). 6. an = O(1) if |an | is bounded by a constant as n . 7. A random sequence Yn is Op (1) if for every > 0 there exists a constant M such that limn P (|Yn | > M ) < as n.
Lecture Notes 9 Asymptotic Theory (Chapter 9) In these notes we look at the large sample properties of estimators, especially the maxi-mum likelihood estimator.
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