STAT 4201 Midterm: STAT 421 OSU Point Estimation III

• School: Ohio State University
• Department: Statistics
• Course: STAT 4201
• Professor: All

Document Summary

Data: random sample from a population of interest: real valued measurements, assumption (hopefully reasonable, model: specified probability distribution f x , involves some unknown parameter(s) . , wish to learn about from the data (estimation) Many estimators for parameter or some function ( )u: some may use all the data, e. g. , Sample based: mean, median, variance: some may ignore data! Desirable properties of estimators: consistent, unbiased. Fisher information: statistic (some function of the data) - summary. May not contain all relevant info. in the data about : statistic(s) that contain all the information about are called sufficient statistic(s) No information lost if only this statistic is stored. Conditional distribution of data given the statistic(s) does not depend on the unknown . Factorization theorem: yields sufficient statistics, e. g. : b. 1 bernoulli ( ) . X i: b. 7 poisson ( ) - X i: c. 7 normal (unknown mean ) . X i: c. 7 normal (unknown mean and variance) - n i i.