Properties of Estimators Statistics: 1.Sufficiency 2.Un-biased 3.Resistance 4.Efficiency Parameters:Describe the population Describe samples. But we use.

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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

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

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

n versus n-1: All permutations SamplemeanVar(n)Var(n-1) 1, , , , , , , , , E=

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

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