I wanted to get some ideas where would one look to approach the following problem:
Gaussian linear models are often insufficient in practical applications, where noise can be heavy-tailed. In this problem, we consider a linear model of the form y(i)=a·x(i)+b+e(i). The e(i) are independent noise from a distribution that depends on x as well as on global parameters; however,the noise distribution has conditional mean zero given x. The goal is to derive a good estimator for the parameters (a) and (b) based on a sample of observed (x, y) pairs. The thing is we only have around 150-170 x,y pairs.
Would really appreciate if someone could point me in the right direction. Thanks