Related Concepts
A pivotal quantity is a function of data, whose underlying population distribution is a member of a parametric family, that is not dependent on the values of the parameters. An ancillary statistic is such a function that is also a statistic, meaning that it is computed in terms of the data alone. Such functions are robust to parameters in the sense that they are independent of the values of the parameters, but not robust to the model in the sense that they assume an underlying model (parametric family), and in fact such functions are often very sensitive to violations of the model assumptions. Thus test statistics, frequently constructed in terms of these to not be sensitive to assumptions about parameters, are still very sensitive to model assumptions.
Read more about this topic: Robust Statistics
Famous quotes containing the words related and/or concepts:
“In the middle years of childhood, it is more important to keep alive and glowing the interest in finding out and to support this interest with skills and techniques related to the process of finding out than to specify any particular piece of subject matter as inviolate.”
—Dorothy H. Cohen (20th century)
“Once one is caught up into the material world not one person in ten thousand finds the time to form literary taste, to examine the validity of philosophic concepts for himself, or to form what, for lack of a better phrase, I might call the wise and tragic sense of life.”
—F. Scott Fitzgerald (1896–1940)