Writing STATA code for estimation of theta in log-likelihood in median regression

[Parinay Gupta]

Hello,
I want to use MLE to estimate theta for Inverse hyperbolic sine transformation in case of median regression. From Pence 2006, the likelihood function is:

As of now, my code gives an error: could not calculate numerical derivatives -- discontinuous region with missing values encountered. Here is my code

 
 sysuse auto.dta cap program drop mylf
program define mylf       
    args  lnf mu sigma  theta
    local y   asinh(`theta' * $ML_y) / `theta'
    quietly replace `lnf' = -ln(2/_N) - ln(abs((normalden((`y' - `mu')/`sigma')) - ln(`sigma'))) - 1 - (1/2)*ln(1+(($ML_y)^2) * ((`theta')^2))
end 
 reg price mpg rep78 headroom trunk matrix b=e(b)
matrix b=b,0 
 ml model lf mylf ( price = mpg rep78 headroom trunk)(sigma:)(theta:)  ml check
ml max

Any help to fix this would be appreciated!