Re: MLE of a restricted RV

On Aug 21, 5:23 pm, Outlier <MTBrenne...@xxxxxxxxx> wrote:
Hi,

I am curious if anyone can suggest a solution to this problem.

I want to find the MLE for an angle, a. The sine of the angle is
normally distributed s.t.
X ~ N( sin(a0), s^2)

Of course, I am interested in the distribution of phi. Making the
normal change of variables requires I restrict the pdf so |X|<1.
Letting:

FX(x|a0) = CDF for X given a0

then I can define the "mixed" pdf:

Case 1 : F(-1|a0) for X=-1
f (y) = Case 2 : Normal PDF for -1<X<1 (using transformation
of rv rule)
where pdf is scaled by F(1|a0)-F(-1|a0)
Case 3 : 1 - F(1|a0) for X=1
Case 4 : 0 |X| > 1

Cases 1 and 3 could be thought of as being equivalent to assigning MLE
= -pi/2 and pi/2 resp.

When you try to find the MLE for a value of X s.t. |X|<1, the problem
you run into is that the scale factor in the denominator of the pdf is
dependent on the parameter of interest a0. When I do calculations with
Mathematica, where I fix a value of X and evaluate the pdf for various
values of a0, the maximum is not typically at a value even remotely
near ArcSin(X).

Is there a way to remedy this problem or a better estimation method
that would work in such a situation?

TIA,

Matt

Look up the von Mises distribution.

.

Relevant Pages

  • MLE of a restricted RV
    ... I want to find the MLE for an angle, ... The sine of the angle is ... then I can define the "mixed" pdf: ... Cases 1 and 3 could be thought of as being equivalent to assigning MLE ...
    (sci.stat.edu)
  • MLE for a restricted rv
    ... I want to find the MLE for an angle, ... The sine of the angle is ... then I can define the "mixed" pdf: ... Cases 1 and 3 could be thought of as being equivalent to assigning MLE ...
    (sci.stat.math)
  • Error in MLE
    ... Then mle but just get error: ... The PDF function returned NaN or infinite values. ... the user-supplied logpdf function 'betalogpdf': ... phat = mlecustom; ...
    (comp.soft-sys.matlab)
  • Re: Why so much interest in pdflatex?
    ... using \includegraphicswithout the file extension is ... I often produce a PS image first and ... then use Adobe Distiller to convert it into a PDF image. ... The two lines only differ in angle setting. ...
    (comp.text.tex)
  • Re: How can i read the stack frames of running process?
    ... intrinsic property is. ... Probably there's an embedded n-dash sized space in "angle". ... this kind of flakiness with PDF isn't that unusual. ... If the result of a search is important, and I have both PDF and ASCII ...
    (comp.lang.c)
Loading