ACN stats affect PETS??

like the title says
does stats affect pet performance? like crit rate determination accuracy and such?

also if i self buff lets say + crit rating. does that buff only affects the actions made my me as a character or by me as an ACN ( me + pet ).
thanks,

I can say that VIT definitely affects topaz's hp. I can only assume that other stats such as INT(at the very least) should also benefit the pets.