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#51 Re: Help Me ! » Two stage least squares » 2011-08-27 19:15:07

lindah

Hi bobbym,

Thank you for looking smile

I was shown that if there was a measurement error in for e.g. X then we could write the error as follows:


where
is the 'true" figure of X
If this were substituted into the original regression we would obtain


So the error term of this regression is affected by
, so there is correlation between X and the error term which isn't ideal for a regression

Does it make it different in this context?

#52 Help Me ! » Two stage least squares » 2011-08-27 18:31:26

lindah
Replies: 13

HI guys,

May I ask if anyone here is a bit of a regression expert?

You are given a dependent variable y, and independent variable x such that the regression would be:

There is the possibility that both x and y have measurement errors in them.
You are also given the lagged (by one period) dataset of x and y (x_1 and y_1 respectively).

How would you go about fixing this error?
______________________________________________________________________________________________________________________
May I ask if my approach is correct?
I would use the lagged data to estimate the true values of x & y, so that the errors are no longer correlated so that the model would look as follows

Then this would be the equivalent of running a two way least squares regression with x_{1} and y_{1} as instrumental variables?

Thank you in advance for any feedback

Regards,
Linda

#53 Re: Help Me ! » MLE and its variance » 2011-08-25 17:28:42

lindah

Hi gAr,

Thank you very much for having a look!!

The second part I've never come across before, though I get similar answers using Hessian and Fisher Information methods

Linda

#54 Help Me ! » MLE and its variance » 2011-08-25 13:52:16

lindah
Replies: 3

Hi guys,

I am back with an annoying MLE as follows (sorry in advance for the length!!!):
http://imageshack.us/photo/my-images/199/83863226.png/

The first part requires developing an MLE for theta.

First I defined the log likelihood of this function as follows:

The differentiated it with respect to theta to obtains

Equating the above to 0 and rearranging it to obtain theta I get:

Do you guys get anything similar?

The second part requires calculating a variance for the estimator so my thoughts were to use the following rules:

where

So I used these following steps:


In the question we were given that
so I substitute this in:

substituting the estimate of theta as derived in the first part gives an answer of:

Thank you in advance for any feedback

#55 Re: Help Me ! » Parameter Estimation: Statistics » 2011-07-13 15:09:40

lindah

Hi bobby,

Yes I did the full 6 days (I'm proud, it was torturous), but back in Sydney now - which is so cold atm.

#56 Re: Help Me ! » Parameter Estimation: Statistics » 2011-07-08 06:42:21

lindah

Hi bobbym,

I think I would be quickly escorted out of Vegas if I tried!
I actually went here for hiking http://www.parks.tas.gov.au/index.aspx?base=1253

#57 Re: Help Me ! » LaTeX editors » 2011-07-06 15:05:40

lindah

I run linux, so use gedit (notepad equivalent) with a latex plugin.

I've seen alot of raving about lyx, but I prefer to work directly with a .tex file

#58 Re: Help Me ! » Parameter Estimation: Statistics » 2011-07-06 15:03:23

lindah

Hi gAr and bobby,

Apologies for delayed response, I've been on a little holiday.

Yes!!! That's the answer. Very interesting you used the mgf instead, its much more efficient!!!
Thank you for laying out an alternative

#59 Re: Help Me ! » Parameter Estimation: Statistics » 2011-06-24 13:34:45

lindah
lindah wrote:

Hi bobby,

Great, thanks for the assistance!! I'll remember to post the answer, when I get it

Looks like we got it wrong bobbym (I secretly blame you, jk) - used the wrong bounds

instead of

Similarly for

:

Calculating the variance:

Substituting this back gives:

#60 Guestbook » Post Exam » 2011-06-24 01:47:25

lindah
Replies: 2

Hi guys,

I'd like to say a BIG thank you for all your help with my stats questions!!!
Crazy exam by crazy lecturer, but you got me all prepped and on the right line of thinking for questions.

My next subject next semester - Stochastic Calculus yikes
You might hear even more from me then, jk

#61 Re: Help Me ! » Point Estimates » 2011-06-21 02:55:36

lindah

Hi gAr,

I think yours is correct as it maintains the sum notation throughout.
I should do it your way, as I initially obtained the same MLE as you before canceling out the "n's" - which I shouldn't have since n and sigma notation are different in this case
I had

Thank you both for your feedback and sharing!!!

#62 Re: Help Me ! » Transformation of variable » 2011-06-21 02:43:50

lindah

Hi bobby,

I am not sure sad

I previously did it that way as per http://www.mathisfunforum.com/viewtopic.php?id=15626, but in post #11 Bob corrected it with the last part of a cdf should be 1.
I am also follows the example I found here (the very last question):
http://www.stat.cmu.edu/~larry/=stat705/test1sol.pdf

#63 Re: Help Me ! » Transformation of variable » 2011-06-21 02:22:08

lindah

Hi;

I'm assuming it is 1 due to the definition of a cdf ranging from [0,1]. Is this a valid approach?

#64 Re: Help Me ! » Transformation of variable » 2011-06-21 01:03:26

lindah

Hi Bob,

That is all we were given for the question (per the past paper I am looking at).

#65 Re: Help Me ! » Joint Density » 2011-06-21 00:31:47

lindah

Hi bobby,

Thanks for the feedback. I have never seen it the way I do it either, but I've never got a scalar as an answer for other similar questions.
Maybe it is that simple, I certainly hope so!!!

For part 4 of the question:
Using part 3) of the question, if X=12, then

However I am uncertain how to proceed to obtain P(Y>8). May I ask if you have any suggestions?

#66 Re: Help Me ! » Joint Density » 2011-06-20 23:39:57

lindah

Yes, that is what I originally got as well, which I do not think is right.

I got a similar question in my assignment just passed, and we had to find the limits by drawing out those bounds, like you would when dealing with double integrals.
So I tried that approach above, but it seems like over-complicating things.

#67 Re: Help Me ! » Moment Generating Moment » 2011-06-20 23:36:55

lindah

Hi gAr,

I've just tried Mathematica again and got the answers. I must have defined too many symbolic relations (I had many notebooks open last time I tried it).

I've just defined 

f[t_] := ((3 t - 1) E^t + (1 - t) E^-t)/(4 t^2)
f'[t] // Simplify
m=f'[t]
Limit[m, t->0]

This is great for me, because the output from Mathematica is much easier to read than Matlab's

#68 Re: Help Me ! » Point Estimates » 2011-06-20 23:31:00

lindah

Hi bobbym,

I've updated post#3 to expand on it a bit.

w.r.t to Mathematica, not at the moment (I seem to have made a rookie mistake), however thank you for asking!!!

#69 Re: Help Me ! » Point Estimates » 2011-06-20 22:49:53

lindah

Hi bobbym,

I first looked for the expectation of the integral from Q1

Then equating


#70 Re: Help Me ! » Moment Generating Moment » 2011-06-20 22:46:11

lindah
gAr wrote:

Hi lindah,

Good news is I can bring a laptop to my exam.

With mathematica?!
It can do most of the things for you!

Yes, I've installed Mathematica (for a regression question using matrices in the exam) and Matlab for finding derivatives.
I tried putting the question I asked in this thread through Mathematica, but it didn't seem to be able to process it.
With Matlab I obtained the same answers as you!

#71 Re: Help Me ! » Joint Density » 2011-06-20 22:32:11

lindah

Hi bobbym,
I am not sure either sad
May I ask what your approach to find the marginal density for y would be?

#72 Help Me ! » Transformation of variable » 2011-06-20 22:23:17

lindah
Replies: 7

In attempting this I arrive at

Then finding the cdf of

I have:
for

So my cdf is

Then the pdf is the derivative of this

All critiques are welcome!!

#73 Help Me ! » Point Estimates » 2011-06-20 22:09:56

lindah
Replies: 8

Hi Guys,
I am attempting another question for my exam as follows:
http://imageshack.us/photo/my-images/32/48188946.png/

For Q1) I used the following limits for my integral

Q2) My final answer is:

Q3) My answer after solving the derivative of the log likelihood

Thank you in advance
Linda

#74 Re: Help Me ! » Moment Generating Moment » 2011-06-20 22:07:45

lindah
gAr wrote:

I used a CAS to get the derivative and the limit.

And yes, if I'm not using a computer, I'd use L'Hôpital's rule.

Hi
Thanks for this, up to this point I had only used Mathematica as CAS software.
I started using Matlab and got this. All this time I'd been performing this work by hand. Good news is I can bring a laptop to my exam.

#75 Re: Help Me ! » Joint Density » 2011-06-20 21:56:57

lindah

Hi bobby and Dragonshade,

Thanks for the confirmation!

Does anyone have an idea about the marginal density of Y?

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