Point Estimation

Point Estimation

Estimatior - any statistic to estimate a characteristic of a population

Unbiased estimator is denoted by: E(T)=α

The most efficient and best estimator for α, is the estimator that:

is unbiased

has the smallest variance

Most Efficient of Population Mean

Unbiased Estimator:

Most Efficient of Population Variance

Best unbiased estimator of population variance: σ̂^2

S^2 = variance of the sample

Can also be noted as

Best Unbiased Estimator of a Probability/Proportion

X~Bin(n,α)

unbiased estimator:

Estimated Standard Error:

p̂=Ps where Ps = sample proportion

Distribution of the Sample Proportion

For both np>5 and nq>5 a continuity correction needs to be used.

If n>30, by C.L.T. :-

Continuity correction for is: if using equation above