Properties of Estimators
Statistics:
1. Sufficiency
2. Un-biased
3. Resistance
4. Efficiency
Parameters: Describe the population
Describe samples.
But we use it to estimate population parameters
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Properties of Estimators - Data Analysis in Psychology - Lecture Slides, Slides of Advanced Data Analysis
Properties of Estimators, Describe the Population, Describe Samples, Estimate Population Parameters, Unbiased Estimator, Example Population, All Permutations, Expected Value, Degrees of Freedom, Describe the Population. These are the important points of Psychology.
Typology: Slides
2012/2013
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Properties of Estimators
Statistics:
- Sufficiency
- Un-biased
- Resistance
- Efficiency Parameters: Describe the population Describe samples. But we use it to estimate population parameters
Sample Variance as an Unbiased estimator Biased UNbiased Example population: σ μ 2 2 =
∑ (^ y − )
n
∑^ y^ =^6 μ^ =^2
2
( ) n y y s
= 2 2 ( ) 1 2 2 − − =
n y y s y: 1, 2, 3
n versus n-1: All permutations
- 1,1 1.0 Sample mean Var(n) Var(n-1)
- 1,2 1.5 .25.
- 1,3 2.0 1.0 2.
- 2,1 1.5 .25.
- 2,2 2.0
- 2,3 2.5 .25.
- 3,1 2.0 1.0 2.
- 3,2 2.5 .25.
- 3,3 3.0
- E= 2.0 .333.
Not all n-1 estimates are “better” than their n counterparts. But, on average, n-1 is superior (Unbiased). Remember
2
E = expected value Degrees of Freedom