Unbiased Least Square Estimate Vs. Biased Maximum Likelihood Estimate
Both
and
are used in different contexts. The former can give an unbiased to estimate when the two groups share an equal population variance. The latter one can give a more efficient to estimate biasedly. Note that the quantities in the right hand sides of both equations are the unbiased estimates.
Read more about this topic: Pooled Variance
Famous quotes containing the words unbiased, square, estimate, biased, maximum and/or likelihood:
“There is not a more disgusting spectacle under the sun than our subserviency to British criticism. It is disgusting, first, because it is truckling, servile, pusillanimoussecondly, because of its gross irrationality. We know the British to bear us little but ill willwe know that, in no case do they utter unbiased opinions of American books ... we know all this, and yet, day after day, submit our necks to the degrading yoke of the crudest opinion that emanates from the fatherland.”
—Edgar Allan Poe (18091845)
“If magistrates had true justice, and if physicians had the true art of healing, they would have no occasion for square caps; the majesty of these sciences would of itself be venerable enough. But having only imaginary knowledge, they must employ those silly tools that strike the imagination with which they have to deal; and thereby, in fact, they inspire respect.”
—Blaise Pascal (16231662)
“Perhaps his might be one of the natures where a wise estimate of consequences is fused in the fires of that passionate belief which determines the consequences it believes in.”
—George Eliot [Mary Ann (or Marian)
“Scientists are humantheyre as biased as any other group. But they do have one great advantage in that science is a self-correcting process.”
—Cyril Ponnamperuma (b. 1923)
“I had a quick grasp of the secret to sanityit had become the ability to hold the maximum of impossible combinations in ones mind.”
—Norman Mailer (b. 1923)
“Sustained unemployment not only denies parents the opportunity to meet the food, clothing, and shelter needs of their children but also denies them the sense of adequacy, belonging, and worth which being able to do so provides. This increases the likelihood of family problems and decreases the chances of many children to be adequately prepared for school.”
—James P. Comer (20th century)