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:
“Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking, love has found. Man judges of nature in relation to itself; the angelic spirit judges of it in relation to heaven. In short to the spirits everything speaks.”
—Honoré De Balzac (1799–1850)
“Skepticism is unbelief in cause and effect. A man does not see, that, as he eats, so he thinks: as he deals, so he is, and so he appears; he does not see that his son is the son of his thoughts and of his actions; that fortunes are not exceptions but fruits; that relation and connection are not somewhere and sometimes, but everywhere and always; no miscellany, no exemption, no anomaly,—but method, and an even web; and what comes out, that was put in.”
—Ralph Waldo Emerson (1803–1882)
“It is a great pity—but ‘tis certain from every day’s observation of man, that he may be set on fire like a candle, at either end—provided there is a sufficient wick standing out.”
—Laurence Sterne (1713–1768)
“Maybe a nation that consumes as much booze and dope as we do and has our kind of divorce statistics should pipe down about “character issues.” Either that or just go ahead and determine the presidency with three-legged races and pie-eating contests. It would make better TV.”
—P.J. (Patrick Jake)