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Properties of Estimators

Properties of Estimators. Parameters:. Describe the population. Statistics:. Describe samples. But we use it to estimate population parameters. Sufficiency Un-biased Resistance Efficiency. Sample Variance as an Unbiased estimator. UNbiased. Biased. Example population:. y: 1, 2, 3.

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Properties of Estimators

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  1. Properties of Estimators Parameters: Describe the population Statistics: Describe samples. But we use it to estimate population parameters • Sufficiency • Un-biased • Resistance • Efficiency

  2. Sample Variance as an Unbiased estimator UNbiased Biased Example population: y: 1, 2, 3

  3. Samples of Two from the above population Sample y: 1, 2 If If

  4. n versus n-1: All permutations

  5. E = expected value Remember Not all n-1 estimates are “better” than their n counterparts. But, on average, n-1 is superior (Unbiased). Degrees of Freedom

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