Relation To Sufficient Statistics
For some parametric families, a complete sufficient statistic does not exist. Also, a minimal sufficient statistic need not exist. (A case in which there is no minimal sufficient statistic was shown by Bahadur in 1957.) Under mild conditions, a minimal sufficient statistic does always exist. In particular, these conditions always hold if the random variables (associated with Pθ ) are all discrete or are all continuous.
Read more about this topic: Completeness (statistics)
Famous quotes containing the words relation to, relation, sufficient and/or statistics:
“Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
—Ralph Waldo Emerson (1803–1882)
“The adolescent does not develop her identity and individuality by moving outside her family. She is not triggered by some magic unconscious dynamic whereby she rejects her family in favour of her peers or of a larger society.... She continues to develop in relation to her parents. Her mother continues to have more influence over her than either her father or her friends.”
—Terri Apter (20th century)
“Cleverness is serviceable for everything, sufficient for nothing.”
—Henri-Frédéric Amiel (1821–1881)
“We already have the statistics for the future: the growth percentages of pollution, overpopulation, desertification. The future is already in place.”
—Günther Grass (b. 1927)