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Stat 223 Introduction to the Theory of Statistics

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Presentation on theme: "Stat 223 Introduction to the Theory of Statistics"— Presentation transcript:

1 Stat 223 Introduction to the Theory of Statistics

2 Chapter 1 1.1 Sampling Distribution from notes
1.2 Central Limit Theorem from notes

3 Proof:

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5 Examples on the weak low of large number

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7 1.3 Order Statistic (p251-p254)

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10 1.4 Exponential Family (p312-p314) one parameter exponential family:

11 k parameter exponential family:

12 The joint distribution of the exponential family

13 Exponential Family (p312-p314)
Example 1: Example 2:

14 Example 3:

15 Homework: Does the following density function belong to the exponential family?

16 Chapter 2 Point Estimation

17 Statistical inference
2. 1 Introduction Statistical inference estimation Point estimation Interval istimation Tests of hypotheses

18 2.2 METHOD OF FINDING ESTIMATORS

19 Notes:

20 2.2.1 Method of Moments

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24 Homework

25 Note:

26 2.2.2 Maximum Likelihood

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31 Note: ln = log

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33 Clarification of the above example

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36 2.3 Properties of Point Estimator 2.3.1mean Squared Error

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43 Cont. case 2:

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47 We have:

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53 2.4 Unbiased estimation

54 2.4.1 Lower bound for variance

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