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Estimation of parameters

Estimation of parameters. Maximum likelihood principle. What has happened was most likely Maximize likelihood wrt parameters to obtain estimates. Examples. Binomial distribution. Observations: k successes in N Bernoulli trials. Poisson distribution. Observations: k 1 , k 2 , …, k N.

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Estimation of parameters

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  1. Estimation of parameters

  2. Maximum likelihood principle What has happened was most likely Maximize likelihood wrt parameters to obtain estimates

  3. Examples

  4. Binomial distribution Observations: k successes in N Bernoulli trials

  5. Poisson distribution Observations: k1, k2, …, kN

  6. Normal distribution Observations: X1, X2, …,XN

  7. Exponential distribution Observations: X1, X2, …,XN

  8. Moment estimators

  9. For our examples moment estimators = maximum likelihood estimators

  10. Are they always the same ? No

  11. Uniform distributionCauchy distribution

  12. Unbiased and biased estimators

  13. Variance of estimatorsminimum variance estimators

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