The basic idea behind MLE is to obtain the most likely values of the parameters, for a given distribution, that will best describe the data. Therefore we create log-likelihood function for N independent obserwations x1,x2, ..., xN. Let's assume that these obserwations come from N people. Let xi follow normal pdf f(x) with unknow mean and variance. I'd like to find this estimators using MLE. Now I split obserwations into two groups. For the first group I know that pdf is f(x) but for the second f(ax), where a - constant. My question is: Can I use MLE for these rather different functions, put them together. I cannot do it separately i.e. for f(x) and for f(ax) (too little sample size). Or more generally: Can I use MLE for one distribution G(x) and other which agrument x is a function G(k(x)). I haven't got the slightest idea how to proof or reject that. I would appreciate Huxley
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