[R] likelihood question not so related to R but probably requires the use of R

From: Leeds, Mark (IED) <Mark.Leeds_at_morganstanley.com>
Date: Mon 23 Oct 2006 - 13:29:37 GMT

I have a question and it's only relation to R is that I probably need R after I understand what to do.  

Both models are delta y_t = Beta + epslion and suppose I have a null hypothesis and alternative hypothesis    

H_0 : delta y_t = zero + epsilon epsilon is normal ( 0, sigmazero^2 )    

H_1 delta y_t = beta + epsilon epsilon is normal ( sigmabeta^2 )    


so, i calculate the MLE's under the null and the alternative as :  

under H_0 beta hat = 0 and sigmazero^2 hat = sum over t ( delta y_t - zero )^2/ (n-1)    

under H_1 beta hat = ( sum of delta y_t ) /n and sigmabeta^2 = sum over t ( delta y_t - beta hat )^2/(n-1)  


what i have blanked out on is how i take the estimates above and test which model is more likely given the data ? I think I used to know this so I apologize if this is a stupid question. I used to take my estimates and th use dnorm or pnorm or one of those but
I can't remember what I did and I can't find my old code. thanks.

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