Re: Lilliefors Test : 40 years

The Lilliefors Test tests whether a distribution is
normal, and is in no way intended to obtained
confidence
limits for the parameters if normal. Similarly, the
Kolmogorov-Smirnov tests tests for a particular
normal;
if one wants confidence intervals for the parameters,
or some of them, use the more classical tests.

A test generally should not be used to test what it
is
not intended to test. K-S tests for a particular
distribution; Lilliefors adjusts the critical values
so that the test operates correctly if the parameters
allowed to vary in testing a form are estimated.

So there is a separate set of critical values if
one is testing for a normal with known variance
and unknown mean, known mean and unknown variance,
or both unknown. Similarly for other distributions;
the asymptotics for a double-exponential with known
scale parameter can be explicitly calculated, as
the restriction on the Brownian bridge consists
in setting it to 0 at 1/2, and for the uniform it
only reduces n by the number of endpoints estimated,
but otherwise, it is hard to obtain except by
simulation.
--
This address is for information only. I do not claim
that these views
are those of the Statistics Department or of Purdue
University.
Herman Rubin, Department of Statistics, Purdue
University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054
FAX: (765)494-0558



If Afonso can publish a paper on Brownian bridges, then I will celebrate the paper on its anniversary in this forum 41 years from now.

Jack
.

Relevant Pages

  • Re: First college FB game you attended
    ... kid, exact year unknown. ... Purdue V. Georgia tech, We had no Idea where Purdue ... "the Democrat and Republican parties are destroying our country right now,They're destroying our political process." ...
    (rec.sport.football.college)
  • Re: is phonological processing digital?
    ... It is unknown. ... The process of recognizing speech is not ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.lang)
  • Re: Is this mathematically justified?
    ... David Rutherford wrote: ... if y=yis a (possibly unknown or unspecified) function of x? ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.math)
  • Re: Getting standard deviation from average for a population
    ... values if the values themseleves were unknown but the their mean and ... are those of the Statistics Department or of Purdue University. ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.stat.math)