Re: Who "invented" the null hypthesis?

"Luis A. Afonso" wrote:
DZ. (not Bob) wrote

Matt Dz. wrote:

*** The term "acceptance interval" is of course correct in case of parameter space being a REAL LINE. However, the "acceptance region" is more general. Regards,
Matt Dz. ***


My response:

WRONG
Do you ignore that the term *interval* could be n-dimensional?

Do you ignore the fact, that the only correct term for n-dimensional case is "... region"?

For example - in case of the p-dimensional multivariate normal distribution, when we want to find the counterpart to CI (which would be the univariate case) for the mean vector, the confidence region will be a p-–dimensional ellipsoid. This is one of the kinds of elliptic confidence regions.

Now I'm curious - how would you call it in your "terminology" - an elliptic confidence interval? ;-))) Because, as you incorrectly state "the term *interval* could be n-dimensional"? ;-)))



Quoting:
***interval box An interval box is a parallelepiped with sides parallel to the n-dimensional Cartesian coordinate axes. ***

Luis, do you know the difference between the "interval" and the "interval box" (just asking)?

Let me provide you with an useful link: http://planetmath.org/encyclopedia/Interval.html

For the definition of the interval, see:
1 W. Rudin, Principles of Mathematical Analysis, McGraw-Hill Inc., 1976.
2 W. Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Inc., 1987.
3 R. Adams, Calculus, a complete course, Addison-Wesley Publishers Ltd., 3rd ed., 1995.
4 L. Råde, B. Westergren, Mathematics Handbook for Science and Engineering, Studentlitteratur, 1995.
5 R.A. Silverman, Introductory Complex Analysis, Dover Publications, 1972.
6 S. Igari, Real analysis - With an introduction to Wavelet Theory, American Mathematical Society, 1998.

Regards,
Matt Dz.


_____licas (Luis A. Afonso)
.

Relevant Pages

  • Re: Easy test of surrogate factoring
    ... Matt Gutting wrote: ... >> The reason is simple, the mathematics doesn't work for them either way, ... >> That's what happens with major math results, ... not that your math can't produce a workable algorithm, ...
    (sci.math)
  • Re: Easy test of surrogate factoring
    ... Matt Gutting wrote: ... >> The reason is simple, the mathematics doesn't work for them either way, ... >> That's what happens with major math results, ... not that your math can't produce a workable algorithm, ...
    (sci.crypt)
  • Re: I have a paper on graph coloring
    ... But in mathematics the practice is ... mostly frowned upon and not all that common. ... Tell Matt why he won't find many takers? ...
    (sci.math)
  • Re: Who "invented" the null hypthesis?
    ... Matt Dz. ... That was actually my response late at night, ... the univariate case) for the mean vector, the confidence region will ... This is the redeeming value of picking out Afonso's errors because ...
    (sci.stat.math)