STAT 3743 Daily Outline
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General case for maximum likelihood
Remarks
- MLE: maximum likelihood estimator
- point estimators of a parameter
- sometimes take logs before differentiating
Example: MLE for geom distribution
More remarks
- can do it for more than one parameter
- sometimes need sophisticated numerical methods
- MLEs not unique, in general
- sometimes an MLE does not exist
- MLEs are just one of many types of point estimator
Definition of unbiased estimator
Example: X-bar is unbiased in the sharks problem
Example: in two-parameter norm case, MLE of variance is biased, but sample variance is unbiased
Confidence intervals for means
why CI's are important for estimation
intuition for the z-interval
Definition of z-interval, confidence interval, confidence coefficient
Example: 90% confidence interval for μ
Remarks
- for fixed confidence, as sample size increases the CI gets shorter
- for fixed sample size, as confidence increases the CI gets wider
Example: SRS(10) from pop'n, find 95% CI for μ
- identify Parameter of interest, in context
- check Assumptions
- choose relevant Name of procedure based on above
- actually calculate the Interval
- state Conclusion, in context of problem
Date: 2010-11-05 14:46:01 EDT
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