[R] maximum likelihood using nlm to estimate 4 variables

[ED]

Hi I need help

I am new to R and am having problems estimating parameters out of 3stage
constrained function.

I have constructed a code as below and my data are two colomns of R_j and
R_m(sample given below). R_j and R_m represents the dependent and
independent variables respectively. The parameters al_j, au_j, b_j , and
sigma_j need to be estimate and there are no initial estimates to them


llik=function(R_j,R_m)
{

LF=if(R_j<
0)sum[ln(1/(2*pi*(sigma_j^2)))-(1/(2*(sigma_j^2))*(R_j+al_j-b_j*R_m))^2] +
if(R_j>
0)sum[ln(1/(2*pi*(sigma_j^2)))-(1/(2*(sigma_j^2))*(R_j+au_j-b_j*R_m))^2] +

if(R_j==0)sum[(ln(%pnorm((au_j-b_j*R_m)/sigma_j)-%pnorm((al_j-b_j*R_m)/sigma_j)))]
}
est.nlm = nlm(llik,0) #not sure what to put for the 4 initial estimates so I
just put 0
est.nlm$estimate

Sample Data
R_j	R_m
0.002	0.026567295
0.003	-0.009798475
0.05	0.008497274
-0.01	0.012464578
-0.0009	0.002896023
0.09	0.000879473
0.01	-0.003194435
0.0006	0.010281122

I will appreciate if you help me to modify my code to get my estimates or
give me any better method to use.

Thank you in advance

Edward
Student: Institute of Actuaries






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