Chapter 6: Point Estimation Flashcards
1
Q
Point Estimate
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2
Q
Point Estimator
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3
Q
General Concepts of Point Estimation
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4
Q
General Concepts of Point Estimation (contd.)
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5
Q
Example 2
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6
Q
Example 2 contd.
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7
Q
Accurate Estimator
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- for some samples, the estimator will yield a larger value while others will underestimate
8
Q
Expected or mean squared error
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9
Q
Unbiasedness
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10
Q
Unbiased Estimators
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11
Q
Unbiased Estimators (contd.)
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- Suppose (theta) is an unbiased estimator;
- then if theta= 100, the (theta-hat) sampling distribution is centered at 100;
- if theta = 27.5, then the (theta-hat) sampling distribution is centered at 27.5, and so on.
12
Q
Recognizing unbiasedness without knowing parameter
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13
Q
Unbiasedness Equation Theorem
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14
Q
Principle of Unbiased Estimation
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15
Q
Calculating Unbiased Estimator
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16
Q
A
17
Q
Estimators with Minimum Variance
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18
Q
Estimators with Minimum Variance (contd.)
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19
Q
Example 7
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20
Q
Example 7 Solution
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21
Q
Example 7 Solution (contd.)
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22
Q
Reporting a Point Estimate: The Standard Error
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23
Q
Example 9
Example 2 continued…
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24
Q
More on The Standard Error
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25
Point Estimation - to summarize
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Point Estimation - to summarize (contd.)
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Formulating Estimators
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The Method of Moments (MoM)
The basic idea of MoM :
* Equate certain **_sample_** characteristics, such as the mean, to the corresponding population expected values.
* Then solving these equations for unknown parameter values yields the estimators.
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The Method of Moments (MoM) (contd.)
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Example 12
31
Maximum Likelihood Estimation
The method of **_maximum likelihood_** was first introduced by R. A. Fisher, a geneticist and statistician, in the 1920s.
Most statisticians recommend this method, at least when the sample size is large, since the resulting estimators have certain desirable efficiency properties.
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Example 15
