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:
“You see, I am alive, I am alive
I stand in good relation to the earth
I stand in good relation to the gods
I stand in good relation to all that is beautiful
I stand in good relation to the daughter of Tsen-tainte
You see, I am alive, I am alive”
—N. Scott Momaday (b. 1934)
“Every word was once a poem. Every new relation is a new word.”
—Ralph Waldo Emerson (1803–1882)
“For which of you, intending to build a tower, sitteth not down first, and counteth the cost, whether he have sufficient to finish it?”
—Bible: New Testament Jesus, in Luke, 14:28.
“He uses statistics as a drunken man uses lamp-posts—for support rather than illumination.”
—Andrew Lang (1844–1912)