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:
“The difference between objective and subjective extension is one of relation to a context solely.”
—William James (1842–1910)
“We must get back into relation, vivid and nourishing relation to the cosmos and the universe. The way is through daily ritual, and is an affair of the individual and the household, a ritual of dawn and noon and sunset, the ritual of the kindling fire and pouring water, the ritual of the first breath, and the last.”
—D.H. (David Herbert)
“They who do not understand that a man may be brought to hope that which of all things is the most grievous to him, have not observed with sufficient closeness the perversity of the human mind.”
—Anthony Trollope (1815–1882)
“July 4. Statistics show that we lose more fools on this day than in all the other days of the year put together. This proves, by the number left in stock, that one Fourth of July per year is now inadequate, the country has grown so.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)